Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ ____ ____ ____ 1. In social research the purpose of statistics is to a. prove that the research theory is correct b. validate the research project design c. manipulate and analyze data d. ensure acceptance by the scientific community 2. Data is the same thing as a. information collected in numerical form b. information collected in any form c. statistics d. proof 3. In the research process, theory a. is unnecessary b. is always fully developed before any data is gathered c. is developed only after the data have been completely analyzed d. attempts to explain the relationship between phenomenon 4. In the language of science, a variable that is thought to be causal is called a.) an independent variable b. a hypothetical variable c. a primary variable d. a dependent variable 5. In time, the ____ variable precedes the ____ variable. a. hypothetical, theoretical b. theoretical, quantitative c. independent, dependent d. dependent, independent 6. An hypothesis states, in part, that "income increases as education increases". In this statement, income is a. the dependent variable b. the independent variable c. the hypothetical variable d. the secondary variable 7. In the research process, the role of statistics is limited because a. numbers can't prove anything b. of possible flaws in research design or method c. the researcher may not be a mathematician d. people lie when answering questionnaires 8. A survey administered to a sample drawn from a local community finds that a person's political party affiliation is related to whether or not they favor an increase in local sales tax (the headline of a newspaper story based on this poll reads: "Republicans support proposed tax increase"). This is an example of the use of a. b. c. d. ____ ____ ____ ____ ____ ____ ____ ____ ____ univariate descriptive statistics inferential statistics multivariate descriptive statistics reductionist statistics 9. Inferential statistics are necessary in social research because a. it may be impossible to find all members of a certain population b. social scientists don't have the time or money to test an entire population c. some of the population might not cooperate d. samples are sometimes accurate representations of the population but can't always be used to generalize 10. Categories of nominal level variables should be a. mutually exclusive to avoid ambiguity in classifying cases b. exhaustive so that every case fits into a category c. relevant to the research goals d. all of the above 11. Which of the following is NOT a nominal level variable? a. level of education b. zip code c. Occupation d. make of auto 12. In addition to saying that one case is different from another, the ordinal level of measurement allows us to a. order categories from high to low b. measure the distance between high and low c. say that one case is more or less than another d. both a and c 13. The variable socioeconomic status ranges from upper class to lower class and is an example of the a. nominal level of measurement b. ordinal level of measurement c. interval-ratio level of measurement d. ratio level of measurement 14. Which of the following can be treated as an interval-ratio variable? a. social security number b. zip code c. Age d. hair color 15. The number of years that a couple has been happily married is an example of a. nominal level data b. ordinal level data c. interval-ratio level data d. ordinary level data 16. Addition and subtraction are completely justified only when variables are a. Nominal b. Ordinal c. interval-ratio d. none of the above 17. A researcher has calculated the mean for a variable that is ordinal in level of measurement. a. This operation is a violation of level of measurement criterion and the results should be disregarded b. This violation of level of measurement criterion is common and results should be treated with caution c. No violation has occurred, this is a perfectly acceptable application of statistics d. This is a mistake: means should never be calculated for ordinal variables Short Answer 18. Below are some items from a survey. For each item, identify the level of measurement and explain your reasoning. a. In what region of the country were you born? __ South __ Northeast __ Midwest __ Far West __ Other __ Born out of Country This question implies what region of USA one was born. Since I was born in Nigeria, I can certainly say that I was born out of the country. b. How many siblings do you have? __7___ I was born into a family of 8, so I have 7 siblings. c. How satisfied are you with the quality of instruction at this institution? __ Very satisfied __ Satisfied __ Dissatisfied __ Very Dissatisfied I assume that the institution being referred to here is the California Southern University; and since I am extremely satisfied with the quality of instruction that I get from this institution, I had to answer \"very satisfied.\" d. How many miles per gallon does your car average? __35___ Due to the long use of my Toyota Corolla car, I have come to realize that it taken an average of 35 miles per gallon. e. People convicted of first degree murder should be executed. __ Strongly Agree __ Agree __ Neither Agree nor Disagree __ Disagree __ Strongly Disagree I answered \"neither agree nor disagree\" because I like to know the state of the person's health first. If the person acted with his/her whole faculty, s/he probably deserves to be executed; but if the person is not in control due to his/her mental state, then s/he probably deserves to live. Chapter 2 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ 1. To calculate a proportion, the number of cases in any category (f) is divided by a. the total number of categories (k) b. the number of cases in all categories (N) c. the cases in that category (f) d. the number of cases in adjacent categories (k-1) 2. Which of the following is an impossible value for a percentage? a. 0% b. 47.458923% c. 110.00% d. 0.05% 3. Forty of every two hundred students attend all of their classes. What percentage of the student body is this? a. 5% b. 50% c. 2% d. 20% 4. To be converted to a percentage, the proportion must be multiplied by a. 10 b. 100 c. 1000 d. any of the above Table 2.1 TABLE 2.1 POLITICAL PARTY MEMBERSHIP IN TWO COMMUNITIES PARTY: COMMUNITY A COMMUNITY B Republican 103 17 Democrat 135 21 Independent 17 15 Socialist 9 11 TOTALS: 264 64 ____ ____ ____ 5. In Table 2.1, which community has the higher proportion of Independents? a. Community A b. Community B c. Neither d. This proportion can't be determined from the information given. 6. In Table 2.1, what percentage of Democrats lives in community B? a. (21 / 64) 100 = 32.8 b. (21 / 328) 100 = 6.4 c. (21 / 156) 100 = 13.5 d. (64 / 264) 100 = 24.2 7. The crude birth rate of a city that has 250 births in a year and a population of 7500 would be found by using which of the following? crude birth rate = (250 / 7500) 1000 crude birth rate = 7500 / 250 crude birth rate = (1000 / 7500) 250 crude birth rate = (250 / 1000) 7500 8. City A (population = 1567 people) had 34 auto thefts last year. City B (population = 34,567) had 40 auto thefts in the same time period and City C (population = 156,980) had 70 auto thefts. Which city had the highest RATE of auto theft? a. City A b. City B c. City C d. More information is needed to answer this question. a. b. c. d. ____ ____ 9. A nation had a birth rate of 20 in 1990. The rate fell to 13 in 2000. What was the percentage change? a. 100 = 35% b. 100 = 54% c. 100 = 35% **d. 100 = 54% ____ 10. Frequency distributions may be compiled for variables measured at which level? a. nominal b. ordinal c. interval-ratio d. all of the above Table 2.2 TABLE 2.2 AGES OF RESPONDENTS Frequency Percentages Class Intervals 18-24 5 24-30 21 30-40 10 TOTAL 36 ____ 11. In Table 2.2, what percentage of cases is in the 18-24 age group? a. (5 / 36) 100 = 13.88% b. (18 / 23) 100 = 78.26% c. (36 / 5) 100 = 7.4% d. (5 / 21) 100 = 23.81% ____ 12. If we added a cumulative percentage column to Table 2.2 and began our calculations with the 18-24 interval, the entry in the 30-40 interval would be a. 10% b. 33.3% c. 37% d. 100% ____ 13. Pie charts show the frequency distribution of a. one variable b. two variables c. three or more variables d. any of the above ____ 14. For a single variable measured at the nominal level, an appropriate graph would be a. a pie chart b. a histogram c. a frequency polygon d. a bivariate table ____ 15. Histograms and line charts or frequency polygons are used with data measured at the a. nominal level b. ordinal level c. interval-ratio level d. any level Short Answer 16. Below are the scores of 25 students on a midterm test. Organize this information into a frequency distribution using a ten point grading scale for class intervals. Include columns for percentages and cumulative percentages. Write a brief description of the distribution. 35 80 99 93 72 45 69 95 67 77 65 71 70 61 71 75 53 82 57 81 87 90 73 74 83 TEST GRADES Class Intervals 59 or less 60 - 69 70 - 79 80 - 89 90 - 100 TOTALS SPSS Questions Frequency Percentage Cumulative Percentage Father's Highest Degree Valid LT High School High School Junior College Missing Percent 37.6 28.3 Valid Percent 46.7 35.2 Cumulative Percent 46.7 81.9 84.0 25 1.7 2.1 Bachelor 121 8.1 10.0 94.0 Graduate 72 4.8 6.0 100.0 Total 1207 80.5 100.0 NAP 181 12.1 93 6.2 DK NA Total Total Frequency 564 425 19 1.3 293 19.5 1500 100.0 17. What is the level of measurement of the variable Father's Highest Degree? 18. What is the difference between the percent and valid percent columns? 19. What percentage of individuals has a father with a Junior College degree? 20. What percentage of individuals has a father with a Bachelors or lesser degree? 21. What percentage of individuals has a father with less than a Junior College degree? 22. What percentage of individuals has a father with a Bachelors or greater degree? Chapter 3 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ 1. The purpose of measures of central tendency is to describe what value of a distribution of scores is a. the most typical or representative b. the most surprising or unexpected c. the most significant or important d. all of the above 2. The three commonly used measures of central tendency (mode, median, and mean) a. will always have the same value b. will always fall in the same order: the mean will have the highest value, followed by the median and the mode. c. define "typical" or "average" in different ways and will usually have different values d. will always fall in the same order: the mean will have the lowest value, the median will always be in the middle and the mode will have the highest value 3. The mode measures "central tendency" in terms of the most a. common score b. central case ____ ____ ____ ____ ____ ____ ____ ____ ____ c. important score d. average case 4. What measure of central tendency would be most appropriate to summarize data about the color of movie star's eyes? a. median b. mode c. mean d. none of the above 5. The grades on a final exam for a statistics class are as follows: 25% As, 35% Bs, 30% Cs, 9% Ds and 1% Fs. The modal grade of the class is a. A b. B c. C d. D 6. It is possible for a variable to have a. one mode b. many modes c. no mode d. all of the above 7. The median represents the score that is a. half of the sum of the other scores b. the most common or frequent c. in the middle d. midway between the highest and lowest scores 8. In a ranked list of 25 scores, the median is the score of a. the 12th case b. the 13th case c. the average of the scores of the 12th and 13th cases d. the average of all of the scores 9. If the scores on a variable are 11, 14, 18, 19, 20, and 25, the median is a. 3 b. 18 c. 18.5 d. 19 10. For ordinal level variables, the most appropriate measure of central tendency is a. the mode b. the median c. the mean d. none of the above 11. The mean defines "central tendency" in terms of the a. most common score b. typical case c. average score d. most likely score 12. On a survey, age was divided into three categories: 1. 2. 3. Younger than 18 18 to 21 Older than 21 The researcher computed the mean age of her respondents by adding up the scores (the 1s, 2s, and 3s) and then dividing by the number of cases. Which of the following statements is true about this situation? a. A mistake has been made because the scores are only nominal in level of measurement and shouldn't be treated as interval-ratio b. Since the scores are nominal in level of measurement, the mean is an appropriate measure of central tendency and no mistake has been made c. Since the scores are interval-ratio in level of measurement, the mean is an appropriate measure of central tendency and no mistake has been made d. A mistake has been made because the scores are ordinal in level of measurement and shouldn't be treated as interval-ratio ____ 13. If a distribution of test scores has a mean of 70 and a median of 80, the distribution has a. a few very high scores b. a mode of 75 c. a negative skew d. a positive skew ____ 14. A distribution of income for a sample of 45 people that consisted of the presidents of the five largest corporations in the United States and forty assembly line workers would be a. Unskewed b. negatively skewed c. positively skewed d. Symmetrical ____ 15. When interval-ratio data are badly skewed, the appropriate measure of central tendency is the a. Mode b. Median c. Mean d. first quartile ____ 16. A researcher is preparing a report and wants to select a measure of central tendency that shows the most common score in a particular distribution. Which statistic should she select? a. Mode b. Median c. Mean d. none of the above Short Answer 17. A math professor is wondering if students today are better or worse than in the past. He has given the same final to this year's class that he gave ten years ago. Compute mean, median, and mode for both classes and write a paragraph summarizing the differences. 35 45 This Year 65 75 87 80 99 93 72 69 95 67 77 56 74 67 90 87 77 51 77 65 86 71 70 61 71 53 82 57 81 90 73 74 83 Ten Years Ago 75 76 89 55 69 91 79 69 98 91 59 79 68 79 95 Statistics Hours Per Day Watching TV N Valid Missing Mean Median Mode Percentiles 25 50 75 1489 11 2.90 2.00 2 2.00 2.00 4.00 18. Is the distribution of the Hours Per Day Watching TV skewed? If yes, positively or negatively? 19. Fill in the blank. 75 percent of people watch ____ hours of television of fewer daily. 20. Why are the median and the 50th percentile equal values? Chapter 4 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ 1. Measures of dispersion provide an indication of the a. typical or most common score b. variety within the distribution of scores c. size of the sample d. adequacy of the selection criteria for the sample 2. Measures of dispersion indicate the degree to which a set of scores is a. Heterogeneous b. Ambiguous c. Average d. Typical 3. If a distribution of scores has a mean of 30 and a range of 0: a. the variance is 30 b. the interquartile range (Q) is 10 c. there is no dispersion in the distribution d. the standard deviation is 1 4. One problem with the range (R) as a measure of dispersion is that it a. is very difficult to calculate b. ignores the most extreme scores c. can be used only for nominal level variables d. is based on only the most extreme scores 5. The second quartile (Q2) is equal in value to a. the mode b. the median c. the mean ____ 6. ____ 7. ____ 8. ____ 9. ____ 10. ____ 11. d. the range If the variance of a distribution is 16, the mean is 12, and the number of cases is 24, the standard deviation is a. 4 b. 6 c. 8 d. 12 If a variable is interval-ratio in level of measurement, the preferred measure of dispersion would be a. the mean b. the range c. the standard deviation d. the percentile As a distribution of scores becomes more variable, the value of the standard deviation a. decreases b. stays the same c. increases d. becomes unpredictable The lower limit for the standard deviation is 0; the upper limit is a. the score of the mean b. the score of the median c. a function of the number of cases d. undefined; there is no upper limit If you calculated the standard deviation for a distribution of 20 scores, removed the 5 highest scores and recalculated, the value of the standard deviation would a. increase b. stay the same c. decrease d. be reduced by five The information below compares the final exam grades for 2 biology classes: Class 1 Class 2 = 80.2 s = 12.1 N = 25 = 81.3 s = 6.7 N = 23 What may we conclude? Class 1 a. is more homogeneous b. is more heterogeneous c. was a better class d. had no grade higher than a 90 ____ 12. The greater the skew of a distribution of scores, a. the lower the value of the standard deviation b. the higher the value of the standard deviation c. the lower the value of the range d. none of the above. Measures of dispersion are not affected by skew. ____ 13. Four students have applied to a special program and only one can be accepted. They have taken a battery of 12 tests and all four students have exactly the same average score. The standard deviation of their test scores are: Student A = 3.12, Student B = 0.27, Student C = 13.45, Student D = 6.45. If consistency of performance is a criteria for acceptance, which of the four students should be selected? a. A b. B c. C d. D Problems 14. The scores below are from the same final exam given in a math class in two different years (see problem #1 at the end of Chapter 3 in this manual). Compute the mean and median (if necessary) and the range and standard deviation of these scores. Using these statistics, describe the differences in the two sets of scores. 35 80 99 93 72 56 74 67 90 87 45 69 95 67 77 77 51 77 65 86 This year 65 71 70 61 71 75 53 82 57 81 87 90 73 74 83 Ten years ago 75 76 89 55 69 90 79 69 98 91 59 79 68 79 95 15. Some information about auto theft rates (number of auto thefts per 100,000 population) for a sample of 178 cities in two different years is summarized below. Express this statistical information in words. What changes were there in the overall shape of the distribution of this variable? In central tendency? In dispersion? Mean = Median = Standard Deviation = 1985 2005 150.32 117.17 125.17 123.01 12.23 7.01 Statistics Size of Place in 1000s N Valid Missing Mean Median Mode Std. Deviation Variance Range Minimum Maximum Percentiles 25 50 75 757 743 360.63 23.00 1 1225.200 1501114 7072 0 7072 4.00 23.00 82.00 The above SPSS output summarizes data from the GSS about the size of peoples' homes in hundreds of square feet. 16. What is the standard deviation of home size among survey respondents? 17. Why are the mean and median so different? 18. If the data maintained the same mean but were less skewed, would the standard deviation be larger or smaller? Chapter 5 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ 1. By definition, the theoretical normal curve is a. Symmetrical b. positively skewed c. negatively skewed d. Empirical 2. The tails of the theoretical normal curve a. intersect with the horizontal axis between the 4th and 5th standard deviation b. intersect with the horizontal axis beyond the 5th standard deviation c. never touch the horizontal axis d. maintain the same distance above the horizontal axis beyond the 3rd standard deviation 3. On all normal curves the area between the mean and ?? 2 standard deviations will be a. 34.13% of the total area b. 95.44% of the total area c. less than 50% of the total area d. 68.26% of the total area ____ ____ ____ ____ ____ ____ ____ ____ 4. Assuming a normal distribution of 1000 cases, how many cases will be farther away from the mean than +3 standard deviations? a. at least 500 b. about 3 c. 327 d. it's impossible to estimate 5. A Z score of +1.00 indicates a score that lies a. one standard deviation unit to the right of the mean b. one standard deviation unit to the left of the mean c. 1/2 of one standard deviation unit on each side of the mean d. any of the above are possible 6. The standardized normal distribution (or Z distribution) has a. a mean of 0 and a standard deviation of 1 b. a mean of 1 and a standard deviation of 0 c. a mean equal to the average of the scores and a standard deviation equal to the mean d. a mean of 1 and a standard deviation of 1 7. If a Z score is 0 then the value of the corresponding raw score would be a. 0 b. the same as the mean of the empirical distribution c. the same as the standard deviation of the empirical distribution d. probably a negative number 8. To find the area above a positive Z score or below a negative Z score you would a. subtract the value of the Z score from the mean b. use the "Area Beyond Z" column of the Z score table c. add the value of the Z score to the area beyond the mean d. add the area between the Z score and the mean to 100% 9. The Z scores of two tests scores are +1.2 and +1.5. To obtain the area between these scores a. subtract the Z scores and find the area of the difference in the Z score table b. find the area between each score and the mean in the Z score table and then subtract the smaller area from the larger area c. find the area between each score and the mean in the Z score table and then subtract the difference between them from 100% d. find the area beyond each score in the Z score table and subtract the difference between the areas from the mean 10. The area between two negative Z scores can be found by a. adding the Z scores and finding the area below the total Z score b. subtracting the Z scores and finding the total area above the total Z score c. finding the area between each Z score and the mean and subtracting the smaller area from the larger d. finding the area between each Z score and the mean and adding the areas 11. If a case is randomly selected from a normal distribution, the score of the case will most likely be a. equal to the mean in value b. close to the mean in value c. at least 1 standard deviation above the mean d. at least 1 standard deviation below the mean ____ 12. A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders. The scores were normally distributed with a mean of 45 and a standard deviation of 7. What is the approximate probability that a randomly selected case from the sample will have a score less than 38? a. .4526 b. .5018 c. .5200 d. .1587 Problem 13. A sample of university students have an average GPA of 2.78 with a standard deviation of 0.45. What is the probability that a randomly selected student will have a GPA a. b. c. d. e. f. less than 3.40? less than 3.78? more than 3.50? more than 2.50? between 2.00 and 3.00? between 3.00 and 3.50? Z score _______ _______ _______ _______ _______ _______ Probability ____ ____ ____ ____ ____ ____ Frequncy 1 2 5 1 0 7 5 5 0 2 5 M e a n = 2 . 7 9 S t d . D v 5 0 3 N 1 , 0 1 02 0 3 0 4 0 5 06 0 A g e W h e n F irs tM a rie d 14. Is the variable Age When First Married roughly normally distributed? 15. Using the normal distribution calculations, 60% of respondents are married before what age? 16. Using the normal distribution calculations, what percentage of people are first married in their 20's? Chapter 6 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ ____ ____ ____ 1. Social scientists gather data from samples instead of populations because a. samples are much larger and more complete b. samples are more trustworthy c. populations are often too large to test d. samples are more meaningful and interesting 2. Statistics are to parameters as a. samples are to populations b. populations are to samples c. medians are to standard deviations d. percentages are to proportions 3. The goal of all techniques for selecting probability samples is to select samples that are a. very large b. non-random c. easily located d. Representative 4. Social scientists use inferential statistics to generalize to populations after they have a. collected a representative sample b. collected all the information possible from the entire population c. collected an EPSEM sample from the population of interest d. collected at least 100 cases from all possible populations 5. The fundamental principle of probability sampling is that a sample selected by ____ is very likely to be ____. a. EPSEM, representative b. stratification, large c. telephone polls, cheap d. clusters, stratified 6. The sampling distribution links the ____ distribution to the ____ distribution. a. stratified, EPSEM b. statistical, empirical c. sample, population d. empirical, real 7. What are the three distributions involved in every application of inferential statistics? a. sample, sampling, and population b. sample, stratification, cluster c. EPSEM, random, probability d. sampling, percentage, normal 8. In a sampling distribution of sample means, most of the sample means will ____ 9. ____ 10. ____ 11. ____ 12. ____ 13. ____ 14. ____ 15. ____ 16. a. cluster around the true population value b. be below the population mean in value c. be above the population mean in value d. not follow any particular pattern The Central Limit Theorem states that as sample size becomes large a. the sampling distribution of sample means approaches normality b. the sampling distribution of sample means becomes larger c. the population distribution becomes normal d. the sample distribution becomes normal When we use larger samples (N > 100) we can assume a normal sampling distribution because of a. common sense b. the Central Limit Theorem c. what we know about the population d. what we know about the sample In comparing a sampling distribution with a population distribution, a. there will always be more variance in the sampling distribution b. there will always be more variance in the population distribution c. as the size of the sample increases the two distributions will become identical d. the two distributions will always be the same Two sample statistics are unbiased estimators. They are a. means and proportions b. means and standard deviations c. medians and modes d. proportions and percentages The probability that an interval estimate does not include the population value is called a. the margin b. alpha c. an error d. the odds An alpha level of 0.05 is the same as a confidence level of a. 99.5% b. 95% c. 90.5% d. 90% To decrease the probability that a confidence interval will NOT include the population parameter a. lower the alpha level b. raise the alpha level c. increase the bias of the sample statistic d. set efficiency to zero A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimate of the parameter at the 95% level is about $175 wide. In this research situation a. we can be 95% confident that the population mean is 42,000 175 b. the sample size is much too small to justify the use of estimation procedures c. the alpha level is 1000 d. the sample mean is $175 ____ 17. In a two person race, if the Republican presidential candidate is projected to attract 44% 3% of the vote and the Democratic candidate is projected to attract 46% 3% of the vote, then a. b. c. d. the Republican is the probable winner the Democrat is the probable winner neither candidate will win a majority of votes in the electoral college the race is "too close to call" Problems 18. Define and distinguish between the sample distribution, the sampling distribution, and the population distribution. How are these three distributions related to each other in inferential statistics? What symbols are used to identify the means and standard deviations of each of the three distributions? 19. Four hundred and thirty two of the 668 respondents questioned said that they favored capital punishment for people convicted of murder. Ten years ago, in response to the same question, 378 out of 703 people were in favor of capital punishment. Has support for capital punishment risen over the ten year period? One-Sample Statistics N Highest Year of School Completed 1496 Mean 13.04 Std. Deviation Std. Error Mean 3.074 .079 One-Sample Test Test Value = 0 t Highest Year of School Completed 164.036 df 1495 Sig. (2-tailed) .000 Mean Difference 13.037 95% Confidence Interval of the Difference Lower Upper 12.88 13.19 20. What is the confidence interval for the mean highest year of school completed? 21. What is the width of the confidence interval? 22. What is the alpha value? 23. What is the confidence level? 24. If nothing else changed, would a higher confidence level lead to a wider or narrower confidence interval? Chapter 7 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ ____ ____ ____ ____ 1. The central problem in the case of one sample hypothesis test is to determine a. if a sample is random b. if sample statistics are the same as those of the sampling distribution c. if parameters are representative of population d. if a sample came from a population with a certain characteristic 2. Like estimation procedures, hypothesis testing involves the risk that the sample a. may not be representative b. may not be biased c. may be too large d. may not be significant 3. To conduct a test of hypothesis with a single sample mean, we must assume a. the sampling distribution is normal b. random sampling c. interval-ratio level of measurement d. all of the above 4. The null hypothesis in the one sample case is a statement of a. agreement with the research hypothesis b. rejection c. acceptance d. no difference 5. If we reject a null hypothesis of "no difference" at the 0.05 level a. the odds are 20 to 1 in our favor that we have made a correct decision b. the null hypothesis is true c. the odds are 5 to 1 in our favor that we have made a correct decision d. the research hypothesis is true 6. The critical region is a. the area under the curve that contains "non-rare" events b. the area under the curve that includes those values of a sample statistic that will lead to rejection of the null. c. a confidence interval d. a law that states that the shape of the sampling distribution is normal 7. In tests of significance, if the test statistic falls in the critical region, we may conclude that a. the population distribution is normal b. the null hypothesis can be rejected c. the research hypothesis is true d. our sample size was too small 8. A sample of people attending a professional football game averages 13.7 years of formal education while the surrounding community averages 12.1. The difference is significant at the .05 level. What could we conclude? a. the null hypothesis should be accepted b. the research hypothesis should be rejected c. the sample is significantly more educated than the community as a whole d. the alpha level is too low 9. A researcher is interested in the effect that neighborhood crime-watch efforts have on the crime rate in the inner city, but he is unwilling to predict the direction of the difference. The appropriate test of hypothesis would be a. one-tailed ____ 10. ____ 11. ____ 12. ____ 13. ____ 14. ____ 15. ____ 16. b. two-tailed c. descriptive d. symmetrical Do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? The appropriate test of hypothesis would be a. a one-tailed test b. a two-tailed test c. cross-sectional d. participant observation In a one-tailed test of hypothesis, the entire ____ should be placed in either the upper or lower tail of the ____ a. critical area, sampling distribution b. sample mean, population distribution c. Z score, critical area d. sampling distribution, sample distribution A one-tailed test of significance could be used whenever a. the researcher can predict a direction for the difference b. the researcher feels like it c. the null hypothesis is thought to be true d. the alpha level exceeds 0.10 With alpha set at .05, the Critical Region for a two-tailed test would begin at 1.96. In a one-tailed test at the same alpha level the Critical Region would begin at a. 1.96 b. 2.58 c. + or 2.30 d. + or 1.65 If we reject a null hypothesis which is in fact true, we a. have made a correct decision b. have made a Type I error c. have made a Type II error d. should have used a one-tailed test The probability of Type I error is a. .01 b. .05 c. the alpha level d. Beta All other things being equal, with which of the following alpha levels would we be most likely to reject the null hypothesis? a. .01 b. .001 c. .05 d. .10 ____ 17. Given that the null hypothesis is actually true, the probability of Type II error is a. .00 b. .05 c. 1.00 d. the alpha level ____ 18. The t distribution, compared to the Z distribution, is a. more skewed b. more peaked for small samples but increasingly like the Z distribution as N increases c. bimodal d. flatter for small sample sizes but increasingly like the Z distribution as N increases ____ 19. Sixty percent of the respondents in a random sample drawn from a neighborhood are Democrats. The community as a whole is 75% Democrat. The difference between sample and population has been tested and the null hypothesis has been rejected. What may we conclude? a. a Type I error has been committed b. a one-tailed test has been used c. the neighborhood is significantly less likely to be Democrat d. the difference is not significant Problems 20. In your own words, define and explain each of the following terms and concepts: a. b. c. d. the null hypothesis Type I (alpha) error Sampling distribution One-tailed test One-Sample Statistics N Ideal Number of Children 965 Mean 2.76 Std. Deviation 1.571 Std. Error Mean .051 One-Sample Test Test Value = 3 Ideal Number of Children t -4.755 df 964 Sig. (2-tailed) .000 Mean Difference -.240 21. What is the null hypothesis tested with the SPSS output above? Alternative hypothesis? 22. Is the test one-tailed or two-tailed? 23. What is the sample standard deviation? 24. Give the results of the hypothesis test and interpret. Chapter 8 95% Confidence Interval of the Difference Lower Upper -.34 -.14 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ ____ ____ ____ 1. The central problem in the case of two-sample hypothesis test is to determine a. if the samples are random b. if sample statistics are the same as those of the sampling distribution c. if the parameters are representative of the populations d. if two populations differ significantly on the trait in question 2. When testing for the significance of the difference between two sample means, the null hypothesis states a. 1 = 2 b. > 0 c. 1 = 2 d. 1 = 2 3. When testing for the significance of the difference between two samples, the null hypothesis reminds us that our interest is on differences between the a. samples b. populations c. sampling distributions d. standard deviations 4. Rejection of the null hypothesis in the two-sample case implies that the a. samples are different on the trait of interest b. populations from which the samples are drawn are different on the trait of interest c. samples are not different on the trait of interest d. populations from which the samples are drawn are not different on the trait of interest 5. When conducting hypothesis tests for two sample means, the test statistic is a. alpha b. the difference in sample means c. the degrees of freedom d. the difference in the population means 6. When conducting hypothesis tests for two sample means, the term 1 2 in the numerator of the formula reduces to zero because a. the standard deviations are calculated first b. the tests are conducted at very low alpha levels c. the samples are independent as well as random d. the null hypothesis is assumed to be true 7. For testing the difference between two sample means, the level of measurement is assumed to be a. nominal b. ordinal c. interval-ratio d. any of the above 8. A researcher conducted a survey to determine if older people have different feelings about abortion than younger people. He used an alpha level of 0.05 (Z critical = 1.96) to test for significance and found that his computed test statistic was 2.76. He may conclude that a. the difference occurred by random chance b. the difference did not occur by random chance c. the samples are not independent d. the alpha level was too low ____ 9. When testing for the significance of the difference between sample means with small samples, the proper sampling distribution is a. the alpha distribution b. the beta distribution c. the Z distribution d. the t distribution ____ 10. Four test of significance were conducted on the same set of results: For test 1: alpha = 0.05, two-tailed test. For test 2: alpha = 0.10, one-tailed test. For test 3: alpha = 0.01, two-tailed test. For test 4: alpha = 0.01, one-tailed test. Which test is most likely to result in a rejection of the null hypothesis? a. Test 1 b. Test 2 c. Test 3 d. Test 4 ____ 11. The larger the sample size, the a. more important the observed difference b. more likely we are to reject the null hypothesis c. less likely we are to reject the null hypothesis d. lower the Z score ____ 12. A difference between samples that is shown to be statistically significant is always a. theoretically important b. practically important c. sociologically important d. none of the above ____ 13. Very large random samples of Catholics and Protestants have been questioned about their opinions on cohabitation. Forty-six percent of the Protestant and 47% of the Catholics approve of males and females living together without being married. The difference has been tested and found to be statistically significant. What is the most reasonable conclusion? a. This is a statistically significant and important difference b. This difference may be statistically significant but it seems unimportant c. This difference is due to random chance d. The researcher should have used sample means rather than proportions in this situation Group Statistics Number of Brothers and Sisters Respondent's Sex Male Female N Mean 3.71 3.71 641 854 Std. Error Mean .115 .104 Std. Deviation 2.915 3.031 Independent Samples Test Levene's Test for Equality of Variances F Number of Brothers and Sisters Equal variances assumed Equal variances not assumed .335 Sig. .563 t-test for Equality of Means t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper -.009 1493 .993 -.001 .156 -.307 .304 -.009 1405.679 .993 -.001 .155 -.305 .303 14. Give the most appropriate null hypothesis for the above SPSS output. 15. Give the most appropriate alternative hypothesis for the above SPSS output. 16. Give the confidence interval for the difference between the population means. 17. Is the test one-tailed or two-tailed? 18. Give and interpret the result of the hypothesis test. 19. In this case, what would a type 1 error mean? Can a type 1 error occur with the above SPSS output? 20. What is the probability the means are equal? Different? Chapter 9 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ 1. The ANOVA test is designed for dependent variables that have been measured at a. the interval-ratio level b. the nominal level c. the ordinal level d. any level of measurement 2. ANOVA may be thought of as an extension of the ____ a. confidence interval estimation procedure b. t test for the significance of the difference between two sample proportions c. t test for the significance of the difference between two sample means d. t test for the significance of the difference between two matched samples 3. ANOVA is appropriate for situations in which a. only nominal level variables are involved b. we are comparing more than two samples or groups c. the independent variable is interval-ration in level of measurement d. there are fewer than two samples 4. A researcher is analyzing regional differences in family size. She has information on number of children for samples of families from four regions. Which of the following would be an appropriate statistical test? a. t test for matched samples b. t test for difference in means c. ANOVA d. Actually, none of the above would work in this situation ____ ____ ____ ____ ____ ____ ____ ____ ____ 5. The null hypothesis for ANOVA states that a. the variables are independent b. the variables are related c. the population means are equal d. the population means are different 6. In the ANOVA test, if the null hypothesis is true a. the sample standard deviations should be zero b. the sample means should be roughly equal in value c. the population means should be very different from each other d. alpha should be less than zero 7. Stated generally, the null hypothesis for the ANOVA test is a. 1 = 2 = 3 = ... = k b. 1 = 2 = 3 = ... = k c. SST = SSB = SSW d. dfb = dfw 8. In an ANOVA test for the significance of the difference in age between three groups, the sample means were 37.56, 37.57, and 37.58. This pattern would be consistent with the assumption that the a. null hypothesis is false b. null hypothesis is true c. research hypothesis is false d. sample standard deviations approach zero 9. If we reject the null hypothesis in a test using analysis of variance, we are concluding that a. the populations from which our samples come are different b. the variable are independent c. the population variances are the same d. the sample means are significantly different 10. The ANOVA test uses means and standard deviations to compare the amount of variation ____ with the amount of variation ____. a. within categories, between categories b. above categories, below categories c. within sample means, between sample means d. within sample standard deviations, between sample standard deviations 11. With the ANOVA test, the ____ the difference between categories, relative to the differences within, the ____ likely that the null hypothesis will be rejected a. smaller, more b. greater, more c. greater, less d. both a and c are true 12. One limitation of the ANOVA test is that it requires a. nominal level dependent variables b. ordinal level independent variables c. very small samples d. interval-ratio dependent variables 13. One limitation of ANOVA is that, when the null hypothesis is rejected, the test a. does not tell us which sample mean(s) is/are different b. tells us nothing about the standard deviations c. does not tell us which population variances are zero d. does not tell us which population variances are greater than zero ANOVA Age When First Married Between Groups Within Groups Total Sum of Squares 810.574 29444.265 30254.839 df Mean Square 202.644 24.722 4 1191 1195 F 8.197 Sig. .000 Post Hoc Tests Multiple Comparisons Dependent Variable: Age When First Married Bonferroni (I) Religious Preference Protestant Catholic Jewish None Other (J) Religious Preference Catholic Jewish None Other Protestant Jewish None Other Protestant Catholic None Other Protestant Catholic Jewish Other Protestant Catholic Jewish None Mean Difference (I-J) Std. Error -1.381* .353 -3.399* 1.052 -1.063 .540 -3.170* .991 1.381* .353 -2.018 1.081 .318 .595 -1.789 1.022 3.399* 1.052 2.018 1.081 2.336 1.155 .229 1.423 1.063 .540 -.318 .595 -2.336 1.155 -2.107 1.100 3.170* .991 1.789 1.022 -.229 1.423 2.107 1.100 Sig. .001 .013 .493 .014 .001 .621 1.000 .802 .013 .621 .434 1.000 .493 1.000 .434 .558 .014 .802 1.000 .558 95% Confidence Interval Lower Bound Upper Bound -2.37 -.39 -6.36 -.44 -2.58 .46 -5.96 -.38 .39 2.37 -5.06 1.02 -1.35 1.99 -4.66 1.08 .44 6.36 -1.02 5.06 -.91 5.59 -3.77 4.23 -.46 2.58 -1.99 1.35 -5.59 .91 -5.20 .99 .38 5.96 -1.08 4.66 -4.23 3.77 -.99 5.20 *. The mean difference is significant at the .05 level. 14. Give the null hypothesis tested with the above SPSS output. 15. Give the alternative hypothesis tested with the above output. 16. Give the results of the hypothesis test and interpret. 17. Which, if any, means appear to be different? Which groups of people appear to get married the later? 18. Why is it beneficial to conduct an ANOVA test as opposed to multiple two-sample t-tests? Chapter 10 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ ____ ____ ____ ____ ____ ____ 1. The popularity of the Chi Square test is largely due to a. easy computations b. the fact that it can be computed only for interval-ratio level variables c. the need to assume a normal sampling distribution d. the relative ease with which the model assumptions can be satisfied 2. Which assumption about level of measurement is made for the Chi square test? a. all variables are at least ordinal in level of measurement b. all variables are at least interval-ratio in level of measurement c. all variables are nominal in level of measurement d. at least one variable must be ordinal in level of measurement 3. To conduct a chi square test, the variables must first be organized into a. a univariate table b. a bivariate table c. a list, which is then ranked d. frequency distributions 4. A bivariate table in which both variables have three categories has a. three cells b. six cells c. nine cells d. thirty-three cells 5. In the context of chi square, variables are independent if a. they are related b. cause and effect can be proved c. the obtained chi square falls in the critical region d. the score of a case on one variable has no effect on the score of the case on the other variable 6. If two variables are independent, the cell frequencies will be a. exactly the same b. concentrated in only two of the cells c. less than the expected frequencies d. determined by random chance 7. In the chi square test of hypothesis, the null hypothesis states that the variables are a. dependent b. independent c. causally related d. non-random 8. The Chi square test is conducted on the assumption that a. the variables are dependent b. the expected frequencies are not produced by random chance c. samples are non-random d. the null hypothesis is true ____ ____ ____ ____ ____ ____ 9. When the null hypothesis in the chi square test for independence is true, there should be a. a large difference between the observed frequencies and the expected frequencies b. little difference between the observed frequencies and the expected frequencies c. no difference between the observed frequencies and the marginals d. no difference between the row and the column marginals 10. Cell frequencies computed under the assumption that the null hypothesis is true are called a. observed frequencies b. experimental frequencies c. expected frequencies d. random frequencies 11. The value of the chi square test statistic is always a. zero or a positive number b. greater than the number of cells in the bivariate table c. equal to or greater than the critical value d. greater than the degrees of freedom 12. The sampling distribution for chi squares is a. shaped like any other normal curve b. not normally distributed c. bimodal d. all of the above 13. In the Chi square test for independence, the null hypothesis and the research hypothesis a. always contradict each other b. always agree with each other c. are never actually stated d. are usually both rejected 14. Chi square is used to test relationships for their a. empirical importance b. logical importance c. statistical significance d. theoretical importance Problem 15. Is support for the proposed anti-smoking law related to political party affiliation? Use the five step model as a guide and write a sentence or two interpreting your results. Don't forget to compute and interpret column percentages. Support: In Favor Neutral Opposed Democrat 36 20 10 66 Party Independent 23 17 18 58 Republican 17 16 36 69 76 53 64 193 Folk Music * Jazz Music Crosstabulation Count Folk Music Total Like It Very Much Like Very Much 32 Like It 79 Mixed Feelings 69 Dislike It 36 Dislike Very Much 13 229 Like It 33 203 139 64 28 467 Jazz Music Mixed Feelings 34 113 143 49 19 358 Dislike It 16 90 64 95 10 275 Dislike Very Much 7 20 16 8 13 64 Total 122 505 431 252 83 1393 Chi-Square Tests Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases Value 114.660a 97.539 16 16 Asymp. Sig. (2-sided) .000 .000 1 .000 df 17.510 1393 a. 1 cells (4.0%) have expected count less than 5. The minimum expected count is 3.81. 16. Give the null hypothesis tested with the above SPSS output. 17. Give the alternative hypothesis tested with the above SPSS output. 18. Give the result of the hypothesis test and interpret. 19. What is the level of measurement of each of the variables compared above? 20. What is the probability liking jazz music and folk music is independent? Dependent? Chapters 11 and 12 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. For ordinal level variables with only a few categories or values, an appropriate measure of association would be a. Spearman's rho b. Gamma c. Chi square d. Cramer's V ____ ____ ____ ____ ____ ____ ____ ____ 2. For ordinal level variables, gamma measures a. the statistical significance of the relationship b. the proportional reduction in error gained by predicting one variable while taking the other into account c. the relative importance of each variable to the association d. all of the above 3. A researcher is interested in the relationship between social class (measured as upper, middle, or lower) and support (measured as strong, moderate, or weak) for a program of welfare reform. An appropriate measure of association for these two variables would be a. Spearman's rho b. Phi c. Pearson's r d. Gamma 4. Gamma ranges from a. 0 to 1.00 b. 1.00 to 100 c. 0.00 to 1.00 d. 1.00 to + 1.00 5. In a negative relationship a. if case A ranks below case B on one variable, case A will rank below case B on the other variable b. if case A ranks above case B on one variable, it will rank below case B on the other variable c. if case A ranks above case B on one variable, it will rank above case B on the other variable d. none of the above 6. A researcher found a gamma of 0.45 between social class and movie attendance, this indicates that a. as social class increases, so does movie attendance b. rich people watch more movies than poor people c. there is no relationship between these variables d. people from higher social classes are less likely to attend movies 7. For a relationship between education and library use, gamma was +0.37. This indicates that a. library use increases with education b. the well educated are more likely to purchase books c. as education goes up, people are less likely to go to the library d. people with limited funds have greater need for free public libraries 8. Gamma is a symmetrical measure of association. This means that a. values of gamma cluster around the center of the range of scores b. gamma is just as likely to be negative as positive c. gamma cannot exceed the value of the highest score d. the value of gamma will be the same regardless of which variable is assumed to be independent 9. Spearman's rho is appropriate for use with a. continuous ordinal variables b. variables whose categories have been collapsed c. tables larger than 2 2 d. negative relationships only ____ 10. Two ordinal level scales measuring religiosity and personal happiness have scores that range from 0 to 100. Which measure of association would be most appropriate to assess the relationship between these two variables? a. chi square b. phi c. gamma d. Spearman's rho ____ 11. Tests of significance tell us if our results are non-random. To investigate the strength and direction of relationships, we must use a. Chi square tests b. ANOVA c. percentages d. measures of association ____ 12. Tests of significance and measures of association provide information about sample data that is a. complimentary b. contradictory c. unnecessary d. redundant ____ 13. Measures of association a. increase our understanding of causal relationships among variables b. provide proof of causal relationships among variables c. enhance our ability to predict from one variable to another d. both a and c ____ 14. If the distribution of the scores of one variable changes across the categories of another variable, the variables a. are associated to some extent b. are related in a way that is statistically significant c. have a cause and effect relationship d. are perfectly associated ____ 15. If social class is a cause of a person's political ideology, then ____ is the independent variable and ____ is the dependent variable. a. class, ideology b. ideology, class c. person, ideology d. information is not sufficient to tell which is independent and which dependent ____ 16. In the case of a perfect association, predictions from one variable to another can be made a. only if variables are measured at the nominal level b. when at least one variable is ordinal c. without error d. only if the relationship is positive ____ 17. For variables measured at the nominal level, measures of association will have a lower limit of ____ and an upper limit of ____. a. 0 ... 100 b. 1 ... +1 c. 0 ... 1 d. 1 ... 0 ____ 18. If the conditional distributions of Y do not change across the categories of X, any measure of association and the maximum difference would be a. 1.00 b. 0.00 c. 0.10 d. 100 ____ 19. If there is a perfect association between sexual attraction and accelerated heartbeat, then a. sex is unhealthy b. there is strong evidence that sexual attraction and accelerated heartbeat are causally related c. if there is no sexual attraction, the heartbeat never accelerates d. whenever the heartbeat accelerates, people become sexually attractive ____ 20. If there is a positive association between two variables, a. as one variable increases in value, the other also increases b. as one variable decreases in value, the other increases c. the researcher can be certain of his conclusions d. neither variable can decrease ____ 21. "As education increases, income rises." This is an example of a(n) a. non-causal relationship b. positive relationship c. negative relationship d. neutral relationship ____ 22. The strength of an association between variables can be shown by computing phi, a measure that is a. appropriate for 2 2 tables b. relatively easy to calculate c. based on chi square d. all of the above ____ 23. For a 3 3 table, the appropriate chi square based measure of association would be a. Cramer's V b. phi c. lambda d. any of the above Attended Sports Event in Last Yr * Visited Art Museum or Gallery in Last Yr Crosstabulation Count Attended Sports Event in Last Yr Total Yes No Visited Art Museum or Gallery in Last Yr Yes No 404 386 198 499 602 885 Total 790 697 1487 Chi-Square Tests Pearson Chi-Square Continuity Correctiona Likelihood Ratio Fisher's Exact Test Linear-by-Linear Association N of Valid Cases Value 79.414b 78.474 80.584 79.361 df 1 1 1 Asymp. Sig. (2-sided) .000 .000 .000 1 Exact Sig. (2-sided) Exact Sig. (1-sided) .000 .000 .000 1487 a. Computed only for a 2x2 table b. 0 cells (.0%) have expected count less than 5. The minimum expected count is 282. 17. Symmetric Measures Nominal by Nominal Ordinal by Ordinal N of Valid Cases Phi Cramer's V Gamma Value .231 .231 .450 1487 Asymp. a Std. Error Approx. T .044 9.214 b Approx. Sig. .000 .000 .000 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. 24. To determine the size of the relationship between visiting art museums or galleries and attending sporting events, which is the most appropriate measure of association? 25. What is the size of the relationship? 26. Does the relationship have a direction? Chapter 13 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. The appropriate measure of association for situations in which both variables are interval-ratio in level of measurement is a. Pearson's r b. gamma c. chi square d. the slope (b) ____ ____ ____ ____ ____ ____ ____ ____ ____ 2. When referring to interval-ratio variables, a commonly used synonym for association is a. probability b. predictability c. correlation d. causation 3. By convention, the independent variable is arrayed along the ____ in a scattergram. a. vertical axis (the ordinate) b. regression line c. horizontal axis (the abscissa) d. calibration line 4. After scores of all cases have been located on a scattergram, a straight line drawn so that it comes as close as possible to touching every score is called the a. regression line b. line of approximation c. cluster line d. scattergram summary 5. A perfect association between variables can be seen on a scattergram when a. all dots lie an equal distance from the regression line b. all dots lie on the regression line c. the regression line forms a right angle at its intersection with the X axis d. the regression line is parallel to the X axis 6. The direction of a relationship between variables can be detected on a scattergram by considering the angle of the regression line. The relationship is a. positive when the line slopes upward from left to right b. positive when the line slopes downward from left to right c. negative when the line slopes upward from left to right d. negative when the line slopes downward from right to left 7. One key assumption of correlation analysis is that the variables have an essentially ____ relationship. a. linear b. non-linear c. curvilinear d. circular 8. The position of the least-squares regression line is defined by two elements: a. the X intercept and the slope of the line b. the X intercept and the Y intercept c. the Y intercept and the slope of the line d. the intersection point of the X and Y axes and the slope of the line 9. The Y intercept is the point where a. the horizontal axis connects to the vertical axis b. the regression line crosses the horizontal axis of the scattergram c. the regression line meets the conditional mean of Y d. the regression line crosses the vertical axis of the scattergram 10. If the slope of a regression line is 1.5, then a. for every unit of change in X there is a change of 1.5 units in Y b. for every unit of change in Y there is a change of 1.5 in X c. the score of each case is 1.5 times higher on Y than on X d. Y causes X ____ 11. If a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be a. 1.00 b. 1.00 c. 0.00 d. 0.45 ____ 12. One important function of the least-squares regression equation is that a. we can use it to tell if a relationship is linear b. it summarizes all possible scores on the two variables c. it makes the scattergram symmetrical d. it allows us to predict Y scores for any value of X ____ 13. If the slope (b) is zero, the value of r a. would also be zero b. would be 1.00 c. would be 1.00 d. cannot be determined from the information given ____ 14. A researcher wants to measure the strength of the association between income (measured in dollars per year) and education (measured in number of years of formal schooling). Which of the following would be the most appropriate measure of association? a. the slope (b) b. gamma c. chi square d. Pearson's r ____ 15. A researcher asked a sample of dual career families about the percentage of the family budget contributed by the wife's job (Y) and the total number of children (X). Pearson's r for this relationship is 0.34. Which of the following is an appropriate interpretation of these results? a. For every dollar contributed by the wife, the number of children increases by .34 b. For every additional child, the wife must work longer hours c. Every additional child lowers the economic wellbeing of the family d. As number of children increase, the percentage of the budget contributed by the wife decreases ____ 16. When working with interval-ratio data, the optimal strategy for predicting Y while ignoring X will be to use the a. mode of the Y scores for every case b. median Y score for every case c. mean Y score for every case d. lowest Y score for every case ____ 17. If we calculate an r of .60, the proportion of the variation of Y that is explained by X is a. .36 b. .40 c. .60 d. .64 Model Summary Model 1 R .013a R Square .000 Adjusted R Square -.001 Std. Error of the Estimate 1.574 a. Predictors: (Constant), Hours Per Day Watching TV ANOVAb Model 1 Regression Residual Total Sum of Squares .412 2375.494 2375.906 df 1 959 960 Mean Square .412 2.477 F .166 Sig. .683a a. Predictors: (Constant), Hours Per Day Watching TV b. Dependent Variable: Ideal Number of Children Coefficientsa Model 1 (Constant) Hours Per Day Watching TV Unstandardized Coefficients B Std. Error 2.789 .081 -.009 .022 Standardized Coefficients Beta -.013 t 34.315 Sig. .000 -.408 .683 a. Dependent Variable: Ideal Number of Children 18. Conduct a full hypothesis test for the presence of a linear relationship. Interpret your results. 19. Write the full linear regression equation. 20. Which is a better predictor of the ideal number of children an individual would like to have, the mean of the variable ideal number of children or the linear regression equation? Chapter 14 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Partial and multiple correlation require data which is a. nominal in level of measurement b. ordinal in level of measurement c. inferential and bivariate d. interval-ratio in level of measurement ____ ____ ____ ____ ____ ____ ____ ____ ____ 2. Two variables are said to have a direct relationship if the partial correlation coefficient is a. the same as the bivariate r b. very different from the bivariate r c. much greater in strength than the bivariate r d. a different sign than the bivariate r 3. Spurious or intervening relationships among variables are indicated when the partial correlation coefficient is a. the same as in the bivariate r b. much weaker than the bivariate r c. much stronger than the bivariate r d. a different sign than the bivariate r 4. Which of the following describes a spurious relationship between X, Y, and Z? a. X causes Z, which causes Y b. Z causes X, which causes Y c. Z has no effect on the relationship between X and Y d. Z causes both X and Y 5. Partial correlation will detect all of the following relationships among variables except a. interaction b. direct relationships c. spurious relationships d. intervening relationships 6. The 'first-order' partial correlation coefficient measures a. the bivariate relationship between X and Y b. the relationship between the dependent and control variables c. the bivariate relationship after controlling for the third variable d. the bivariate relationship after controlling for the fourth variable 7. A Pearson's r calculated for the bivariate relationship between X and Y is .50. After controlling for Z, the partial correlation coefficient is .49. This outcome would be evidence of a(n) ____ relationship between X and Y. a. direct b. spurious c. interactive d. negative 8. Which of the following would be consistent with a direct relationship between X and Y? a. Pearson's r is .17, partial correlation coefficient is .16 b. Pearson's r is .78, partial correlation coefficient is .50 c. Pearson's r is .10, partial correlation coefficient is .20 d. Pearson's r is .00, partial correlation coefficient is .00 9. With two independent variables, the least-squares multiple regression equation would a. Y = a + bX2 b. Y = a + b + X1 + X2 c. Y = b1X1 + b2X2 d. Y = a + b1X1 + b2X2 10. One advantage of the technique of multiple regression is that it allows the ____ effects of the ____ variables to be investigated. a. combined, independent b. separate, independent c. combined, control d. separate, dependent ____ 11. The regression equation for a particular relationship is Y = 10 + (.78) X 1 + (.54) X2. Which conclusion is consistent with this equation? a. The Y intercept is zero b. Neither independent variable has an important relationship with Y c. A value for a (the Y intercept) needs to be calculated before the equation can be interpreted d. The two independent variables have opposite effects on the dependent ____ 12. The coefficient of multiple determination (R2) shows a. the effect of the control variable after removing the independent from the equation b. essentially the same thing as a partial correlation coefficient c. the combined effects of all independents on the dependent d. the zero-order relationships after controlling for the independents ____ 13. The techniques of multiple correlation and regression can be used a. as long as the total number of variables is not greater than three b. as long as the ind