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statistics

Questions and Answers of Statistics

In a study of left-handedness as a possible inherited trait, the data in the table below were obtained. Use a 0.01 significance level to test the claim that left-handedness is independent of parental
A X2 test involving a 2 x 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-2. Using the claim and table in Example 4, verify that the X2 test
The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates€™s correction for continuity in cells with an expected
The table below lists auto fatalities by day of the week for a recent year. Minitab results are also shown. Use a 0.01 significance level to test the claim that auto fatalities occur on the different
When certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more Os or 5s. If we use
Listed below are the numbers of weather-related deaths in a recent year. Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same
A study was conducted of 531 persons injured in bicycle crashes, and randomly selected sample results are summarized in the accompanying table. The TI-83/84 Plus calculator results also are shown. At
Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. Does the
Winning-team data were collected for teams in different sports, with the results given in the accompanying table. Use a 0.05 level of significance to test the claim that home/visitor wins are
Review Exercise 3 involved weather-related deaths. Among the 489 deaths included in the table, 325 are males. Use a 0.05 significance level to test the claim that among those who die in
In an American Express survey of 1000 adults 18 and older, 62% said that cigarettes should cost more to help offset potential negative health effects. Use the sample data to construct a 95%
Listed below are the ages of randomly selected patients in intensive care units. Find the mean, median, and standard deviation. Based on the results, is an age of 16 years unusual? Why or why not?
Use the sample of ages from Exercise 3 to construct a 95% confidence interval estimate of the mean age of the population of ICU patients. Do the confidence interval limits contain the value of 65.0
The table below lists the numbers of registered pleasure boats (thousands) in Florida and the numbers of watercraft-related manatee deaths for each year of the past decade.a. Test for a linear
When designing cars and aircraft, we must consider the forward grip reach of women. Women have normally distributed forward grip reaches with a mean of 686 mm and a standard deviation of 34 mm. a. If
In a USA Today survey of 456 subjects, 269 agreed that honesty is always the best policy. Assume that we plan to use the survey results to estimate the proportion of the population who believe that
a. What characteristic of the data: above indicates that we should use one-way analysis of variance?b. If the objective is to test the claim that the three size categories have the same mean chest
Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don€™t we use three separate hypothesis tests for µ1 = µ2, µ1 =
If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude?Assume that we plan to use a 0.05 significance level
Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with measured verbal IQ scores, we get the accompanying
Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with the full IQ scores, we get the accompanying Excel
Data Set 14 in Appendix B lists highway fuel consumption amounts (mi/gal) for cars categorized by size (small, midsize, large). If we use those highway fuel consumption amounts arranged into the
Data Set 14 in Appendix B lists city fuel consumption amounts (mi/gal) for cars categorized by size (small, midsize, large). If we use those city fuel consumption amounts arranged into the three
Use chest deceleration data for three different size categories (small, midsize, large). The data are from a standard crash test and they are listed in Data Set 13 in Appendix B. If we use the head
Use chest deceleration data for three different size categories (small, midsize, large). The data are from a standard crash test and they are listed in Data Set 13 in Appendix B. If we use the pelvis
Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile
Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer€™s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch
Weights (kg) of poplar trees were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted
Weights (kg) of poplar trees were obtained from trees planted in a sandy and dry region. The trees were given different treatments identified in the table below. The data are from a study conducted
Refer to Data Set 10 in Appendix B and use the amounts of nicotine (mg per cigarette) in the king-size cigarettes, the 100-mm menthol cigarettes, and the 100-mm non-menthol cigarettes. The king-size
Refer to Data Set 9 in Appendix B and use the measured serum cotinine levels (in mg/mL) from the three groups of subjects (smokers, nonsmokers exposed to tobacco smoke, and nonsmokers not exposed to
Shown below are partial results from using the Bonferroni test with the sample data from Exercise 13. Assume that a 0.05 significance level is being used.a. What do the displayed results tell us?b.
If we have a goal of using the data described in Exercise 1 to (1) determine whether size of a car has an effect on the load measurements and (2) to determine whether the location of the femur (left
What is an interaction between two factors? In general, when using two way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?
If we use the data described in Exercise 1 with two-way analysis of variance, we get the accompanying display. What do you conclude?
The following table lists results from car crash tests. The listed values are measures of chest deceleration (in g) categorized by type (whether the car is foreign or domestic) and car size (small,
Example 1 in this section used performance IQ scores from Data Set 5 in Appendix B for two-way analysis of variance with the factors of sex (male, female) and measured blood lead level (low, medium,
Listed below are ratings of pancakes made by experts. Different pancakes were made with and without a supplement and with different amounts of whey. The results from two-way analysis of variance are
The following table lists measures of self-esteem obtained from a student project as supervised by Jannay Morrow at Vassar College (based on data from Richard Lowry). The objective of the project was
The following table lists pulse rates obtained from Data Set 1 in Appendix B. Use a 0.05 significance level and apply the methods of two-way analysis of variance. What do you conclude?
Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?a. The same constant is added to each sample
Data Set 14 in Appendix B includes highway fuel consumption amounts for cars with 4 cylinders, 6 cylinders, and 8 cylinders. Analysis of variance is used with the highway fuel consumption amounts
Weights (kg) of poplar trees were obtained from trees planted in one region that was rich and moist and a second region that was sandy and dry. The trees were given different treatments as identified
Data Set 10 in Appendix B includes the amounts of tar (mg per cigarette) in the king-size cigarettes, the 100-mm menthol cigarettes, and the 100-mm nonmenthol cigarettes. The king-size cigarettes are
The table below lists body temperatures obtained from randomly selected subjects. The temperatures are categorized according to gender and whether the subject smokes. Using a 0.05 significance level,
Descriptive Statistics Include appropriate units in all answers. a. Find the mean for each of the three groups. b. Find the standard deviation for each of the three groups. c. Find the variance for
Treating the data as samples from larger populations, test the claim that there is a difference between the mean for presidents and the mean for British monarchs.
Use the longevity times for presidents and determine whether they appear to come from a population having a normal distribution. Explain why the distribution does or does not appear to be normal.
Use the longevity times for presidents and construct a 95% confidence interval estimate of the population mean.
The display below results from using the one-way analysis of variance test.a. What is the null hypothesis?b. Assuming a 0.05 significance level, what conclusion is indicated by the displayed results?
Listed below are weights (kg) of eight male college students in September and April of their freshman year (from Data Set 4 in Appendix B).a. Test for a linear correlation between September weights
Based on Data Set 1 in Appendix B, assume that adult females have blood platelet counts that are normally distributed with a mean of 280 and a standard deviation of 65. a. Find the probability that
Today reported about an Adecco Staffing survey of 1000 randomly selected adults. Among those respondents, 20% chose health benefits as being most important to their job. a. What is the number of
Shown below is a histogram of digits selected in California€™s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.a. If
The bars in the histogram included with Exercise 9 depict these frequencies: 21, 19, 15, 18, 24, 18, 16, 24, 30, and 15. Test the claim that the digits are selected from a population in which the
Sign Test for Freshman 15 The table below lists some of the weights from Data Set 4 in Appendix B. Those weights were measured from college students in September and later in April of their freshman
An important step in conducting the sign test is to determine whether the sample data contradict the alternative hypothesis H1 For the sign test described in Exercise 1, identify the null hypothesis
Positive signs: 856; negative signs: 151; ties: 57 (from a Pew Research Center poll of adults who were asked if they know what Twitter is)Assume that matched pairs of data result in the given number
Positive signs: 172; negative signs: 439; ties: 0 (from challenges to referee calls in the most recent U.S. Open tennis tournament) Assume that matched pairs of data result in the given number of
Listed below are ages of actresses and actors at the times that they won Oscars. These 10 matched pairs are the first 10 from Data Set 11 in Appendix B. The data are paired according to the years
Repeat Exercise 9 using all of the 82 pairs of ages in Data Set 11 from Appendix B. For that data set, there are 16 positive signs, 64 negative signs, and 2 ties.Use the sign test for the data
Refer to Data Set 12 in Appendix B and use the heights of U.S. presidents and their main opponents in the presidential campaigns to test the claim that there is no difference. Use a 0.05 significance
Example 2 using the following times for American Airlines Flight 19.Use the sign test for the data consisting of matched pairs.
The Genetics and IVF Institute conducted a clinical trial of its methods for gender selection. As of this writing, 239 of 291 babies born to parents using the YSORT method were boys. Use a 0.01
A study addressed the issue of whether women have the ability to predict the sex of their babies. Among 104 recruited subjects, 53% correctly guessed the sex of the baby. Use a 0.05 significance
At the age of 9, Emily Rosa tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, then she asked the
In a USA Today poll, people responded to this question “Are today’s NFL (football) games too long?” Among the respondents with a definitive answer, 242 answered yes and 396 answered no. Use a
Refer to Data Set 21 in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use a 0.01 significance
Refer to Data Set 16 in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 1.00. Refer to the indicated data set in Appendix B and
Refer to Data Set 19 in Appendix B for the amounts (in oz) in cans of regular Coke. The cans are labeled to indicate that the contents are 12 oz of Coke. Use a 0.05 significance level to test the
Refer to Data Set 11 in Appendix B for the ages of actresses at the time that they won Oscars in the category of Best Actress. Use a 0.05 significance level to test the claim that the median age of
In the sign test procedure described in this section, we exclude ties. A second approach is to treat half of the 0s as positive signs and half as negative signs. With a third approach, in two-tailed
The following table lists some of the weights from Data Set 4 in Appendix B. Those weights were measured from college students in September and later in April of their freshman year. Assume that we
For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:a. Differences db. The ranks corresponding to the nonzero values of |d|c. The
Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.05 significance level.
Using all of the 82 pairs of ages in Data Set 11 from Appendix B. For that data set, there are 16 positive signs, 64 negative signs, and 2 ties.Use the Wilcoxon signed-ranks test to test the claim
Refer to Data Set 12 in Appendix B and use the heights of U.S. presidents and their main opponents in the presidential campaigns to test the claim that there is no difference. Use the Wilcoxon
Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.05 significance level.
Refer to Data Set 21 in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. the quarters are supposed to have a median weight of 5.670g. Use a 0.01 significance
Refer to Data Set 16 in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 1.00. Use the Wilcoxon signed-ranks test for the claim
Refer to Data Set 19 in Appendix B for the amounts (in oz) in cans of regular Coke. The cans are labeled to indicate that the contents are 12 oz of Coke. Use a 0.05 significance level to test the
Refer to Data Set 11 in Appendix B for the ages of actresses at the time that they won Oscars in the category of Best Actress. Use a 0.05 significance level to test the claim that the median age of
a. If we have sample paired data with 75 nonzero differences, what are the smallest and largest possible values of T? b. If we have sample paired data with 75 nonzero differences, what is the
Refer to the sample data in Exercise 1. Assuming that we use the Wilcoxon rank-sum test with those data, identify the null hypothesis and all possible alternative hypotheses.
Refer to Table 13-2 in Section 13-1 and identify the efficiency of the Wilcoxon rank-sum test. What does that value tell us about the test?
Use the sample data given in Exercise 1 and test the claim that arrival delay times for Flight 19 and Flight 21 have the same median. Use a 0.05 significance level.
Listed below are samples of taxi-out times (min) for American Airlines Flights 19 and 21. Use the sample data to test the claim that taxi-out times for Flight 19 and Flight 21 have the same median.
The sample data below are changes in LDL cholesterol levels in clinical trials of Lipitor (atorvastatin). It was claimed that Lipitor had an effect on LDL cholesterol. Negative values represent
Listed below are amounts of strontium-90 in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979. Use a 0.05 significance level to test the
Data Set 5 in Appendix B lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a
Data Set 5 in Appendix B lists performance IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood.
Data Set 21 in Appendix B lists weights (g) of pre-1964 quarters and post-1964 quarters. Use a 0.05 significance level to test the claim that the samples are from populations with the same median.
Data Set 19 in Appendix B lists weights (lb) of the cola in cans of regular Coke and diet Coke. Use a 0.05 significance level to test the claim that the samples are from populations with the same
The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the
Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the test
Listed below are full IQ scores from simple random samples of subjects with low lead exposure, medium lead exposure, and high lead exposure. In using the Kruskal-Wallis test, we must rank all of the
For the data given in Exercise 1, identify the values of n1, n2, n3, and N.
Refer to Table 13-2 in Section 13-1 and identify the efficiency of the Kruskal Wallis test. What does that value tell us about the test?
Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile
Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer€™s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch

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