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essentials of statistics

Questions and Answers of Essentials Of Statistics

Describe how the standard error of M is calculated, explain what it measures, describe how it is related to the standard deviation for the population, and use this information to determine the
Calculate the z-score for a sample mean.
Describe the circumstances in which the distribution of sample means is normal and, in these circumstances, nd the probability associated with a specic sample.
Describe how the magnitude of the standard error is related to the size of the sample and determine the sample size needed to produce a specied standard error or the new standard error produced by a
Explain how the distribution of sample means can be used to evaluate a treatment effect by identifying likely and very unlikely samples, and use this information to determine whether a specic sample
If all the possible random samples, each with n 5 9 scores, are selected from a normal population with µ 5 80 and s 5 18, and the mean is calculated for each sample, then what is the average value
All the possible random samples of size n 5 2 are selected from a population with m 5 40 and s 5 10 and the mean is computed for each sample. Then all the possible samples of size n 5 25 are selected
If all the possible random samples of size n 5 25 are selected from a population with m 5 80 and s 5 10 and the mean is computed for each sample, then what shape is expected for the distribution of
If random samples, each with n 5 4 scores, are selected from a normal population with m 5 80 and s 5 10, then what is the expected value of the mean for the distribution of sample means?a. 2.5b. 5c.
If random samples, each with n 5 9 scores, are selected from a normal population with m 5 80 and s 5 18, and the mean is calculated for each sample, then how much distance is expected on average
A sample of n 5 4 scores has a standard error of 12.What is the standard deviation of the population from which the sample was obtained?a. 48b. 24c. 6d. 3
A sample of n 5 16 scores is obtained from a population with m 5 70 and s 520.If the sample mean is M 5 75, then what is the z-score corresponding to the sample mean?a. z 5 0.25b. z 5 0.50c. z 5
A random sample of n 5 4 scores is obtained from a normal population with m 5 20 and s 5
What is the probability of obtaining a mean greater than M 5 22 for this sample?a. 0.50b. 1.00c. 0.1587d. 0.3085
A random sample of n 5 4 scores is obtained from a normal population with m 5 40 and s 56.What is the probability of obtaining a mean greater than M 5 46 for this sample?a. 0.3085b. 0.1587c. 0.0668d.
Which of the following would cause the standard error of M to get smaller?a. Increasing both the sample size and standard deviationb. Decreasing both the sample size and standard deviationc.
A sample obtained from a population with s 5 10 has a standard error of 2 points. How many scores are in the sample?a. n 5 5b. n 5 10c. n 5 20d. n 5 25
A random sample is selected from a population with m 5 80 and s 520.How large must the sample be to ensure a standard error of 2 points or less?a. n $ 10b. n $ 25c. n $ 100d. It is impossible to
A sample is obtained from a population with m 5 100 and s 520.Which of the following samples would produce the z-score closest to zero?a. A sample of n 5 25 scores with M 5 102b. A sample of n 5 100
For a normal population with m 5 80 and s 5 20, which of the following samples is least likely to be obtained?a. M 5 88 for a sample of n 5 4b. M 5 84 for a sample of n 5 4c. M 5 88 for a sample of n
For a sample selected from a normal population with m 5 100 and s 5 15, which of the following would be the most extreme and unrepresentative?a. M 5 90 for a sample of n 5 9 scoresb. M 5 90 for a
Briefly define each of the following:a. Distribution of sample meansb. Central limit theoremc. Expected value of Md. Standard error of M
A sample is selected from a population with a mean of m 5 65 and a standard deviation of s 5 15.a. If the sample has n 5 9 scores, what is the expected value of M and the standard error of M?b. If
Describe the distribution of sample means (shape, mean, standard error) for samples of n 5 64 selected from a population with a mean of m 5 90 and a standard deviation of s 5 32.
Under what circumstances is the distribution of sample means definitely a normal distribution?
A random sample is selected from a population with a standard deviation of s 5 18.a. On average, how much difference should there be between the sample mean and the population mean for a random
For a sample of n 5 16 scores, what is the value of the population standard deviation (s) necessary to produce each of the following standard error values?a. sM 5 8 pointsb. sM 5 4 pointsc. sM 5 1
For a population with a mean of m 5 40 and a standard deviation of s 5 8, find the z-score corresponding to each of the following samples.a. X 5 34 for a sample of n 5 1 scoreb. M 5 34 for a sample
A sample of n 5 25 scores has a mean of M 5 68.Find the z-score for this sample:a. If it was obtained from a population with m 5 60 and s 5 10b. If it was obtained from a population with m 5 60 and s
A population forms a normal distribution with a mean of m 5 85 and a standard deviation of s 5 24.For each of the following samples, compute the z-score for the sample mean.a. M 5 91 for n 5 4
Scores on a standardized reading test for fourth-grade students form a normal distribution with m 5 60 and s 5 20.What is the probability of obtaining a sample mean greater than M 5 65 for each of
Scores from a questionnaire measuring social anxiety form a normal distribution with a mean of m 5 50 and a standard deviation of s 5
What is the probability of obtaining a sample mean greater than M 5 53,a. for a random sample of n 5 4 people?b. for a random sample of n 5 16 people?c. for a random sample of n 5 25 people?
A normal distribution has a mean of m 5 54 and a standard deviation of s 5 6.a. What is the probability of randomly selecting a score less than X 5 51?b. What is the probability of selecting a sample
A population has a mean of m 5 30 and a standard deviation of s 5 8a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M 5 32 for a sample of
For random samples of size n 5 16 selected from a normal distribution with a mean of m 5 75 and a standard deviation of s 5 20, find each of the following:a. The range of sample means that defines
The distribution exam grades for an introductory psychology class is negatively skewed with a mean of m 5 71.5 and a standard deviation of s 5 12.a. What is the probability of selecting a random
By definition, jumbo shrimp are those that require between 10 and 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages m 5 12.5 with a standard deviation of s
For a population with a mean of m 5 72 and a standard deviation of s 5 10, what is the standard error of the distribution of sample means for each of the following sample sizes?a. n 5 4 scoresb. n 5
For a population with s 5 16, how large a sample is necessary to have a standard error that isa. less than 8 points?b. less than 4 points?c. less than 2 points?
If the population standard deviation is s 5 10, how large a sample is necessary to have a standard error that isa. less than 5 points?b. less than 2 points?c. less than 1 point?
Jones, Thomas, and Piper (2003) conducted a study to evaluate the effect of alcohol on judgments of attractiveness for members of the opposite sex. Male college students who had either no alcohol or
A normal distribution has a mean of m 5 60 and a standard deviation of s 5 12.For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a
A random sample is obtained from a normal population with a mean of m 5 76 and a standard deviation of s 5 20.The sample mean is M 5 84.a. Is this a representative sample mean or an extreme value for
A sample of n 5 36 scores is selected from a normal distribution with a mean of m 5 65.If the sample mean is M 5 59, then compute the z-score for the sample mean and determine whether the sample mean
Define the terms population, sample, parameter, and statistic; describe the relationships between them; and identify examples of each.
Define the two general categories of statistics, descriptive and inferential, and describe how they are used in a typical research study.
Describe the concept of sampling error and explain how sampling error creates the fundamental problem that inferential statistics must address.
Explain why operational denitions are developed for constructs and identify the two components of an operational denition.
Describe discrete and continuous variables and identify examples of each.
Dene real limits and explain why they are needed to measure continuous variables.
Compare and contrast the four scales of measurement (nominal, ordinal, interval, and ratio) and identify examples of each.
Describe, compare, and contrast descriptive, correlational, experimental, and nonexperimental research, and identify the data structures associated with each.
Define independent, dependent, and quasi-independent variables and recognize examples of each.
Identify what is represented by each of the following symbols: X, Y, N, n, and o.
Perform calculations using summation notation and other mathematical operations following the correct order of operations.
A researcher is interested in the fast-food eating habits of American college students. A group of 50 students is interviewed and the researcher finds that these students eat an average of 2.3
A researcher is curious about the average distance traveled by Canada geese during peak fall migration in the state of New York. The entire group of Canada geese in the state is an example of a .a.
What term is used for the statistical techniques that use sample data to draw conclusions about the population from which the sample was obtained?a. population statisticsb. sample statisticsc.
The SAT is standardized so that the average score on the verbal test is 500 each year. If you select a group of 100 graduating seniors who have taken the verbal SAT, what value would be obtained for
What is an operational definition?a. A definition of a hypothetical construct.b. A method for measuring a hypothetical construct.c. A method for measuring and defining a hypothetical construct.d.
A researcher studies the factors that determine the number of jobs adults have in a lifetime. The variable, number of jobs, is an example of a(n)variable.a. discreteb. continuousc. nominald. ordinal
When measuring height to the nearest half inch, what are the real limits for a score of 69.0 inches?a. 68 and 70b. 68.5 and 69.5c. 68.75 and 69.75d. 68.75 and 69.25
Ranking a group of cities in terms of “quality of life” would be an example of measurement on a(n) scale of measurement.a. nominalb. ordinalc. intervald. ratio
In a correlational study, how many variables are measured for each individual and how many groups of individuals are in the study?a. One variable and one groupb. One variable and two groupsc. Two
A research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman,
A recent study reports that infant rats fed a diet containing genetically modified grains reached an adult weight 10% greater than their litter-mates raised on a regular diet. For this study, what is
What value is represented by the uppercase letter N?a. the number of scores in a populationb. the number of scores in a samplec. the number of values to be added in a summation problemd. the number
What is the value of o(X 1 1) for the following scores: 0, 1, 4, 2?a. 8b. 9c. 11d. 16
What is the last step in the calculation of (oX)2?a. Square each score.b. Add the scores.c. Square the sum of the scoresd. Add the squared scores.
*A researcher is interested in the texting habits of high school students in the United States. The researcher selects a group of 100 students, measures the number of text messages that each
A tax form asks people to identify their age, annual income, number of dependents, and social security number. For each of these three variables, identify the scale of measurement that probably is
Four scales of measurement were introduced in this chapter, from simple classification on a nominal scale to the more informative measurements from a ratio scale.a. What additional information is
The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at ages 2 and 4 compared to children who drank whole or
Gentile, Lynch, Linder, and Walsh (2004) surveyed over 600 eighth- and ninth-grade students asking about their gaming habits and other behaviors. Their results showed that the adolescents who
Stephens, Atkins, and Kingston (2009) conducted an experiment in which participants were able to tolerate more pain when they were shouting their favorite swear words than when they were shouting
Ackerman and Goldsmith (2011) compared learning performance for students who studied material printed on paper versus students who studied the same material presented on a computer screen. All
There is some evidence that people with a visible tattoo are considered to be less attractive than are people without a visible tattoo. Resenhoeft, Villa, and Wiseman (2008) showed one group of
Guéguen and Jacob (2012) asked waitresses to wear different colored T-shirts on different days for a six-week period and recorded the tips left by male customers. The results show that male
For the following scores, find the value of each expression:a. oXb. (oX)2c. oX 2 2d. o(X 2 2)X 32 42
For the following set of scores, find the value of each expression:a. oX2b. (oX)2c. o(X 1 1)d. o(X 1 1)2 X1 24 13
For the following set of scores, find the value of each expression:a. oXb. (oX)2c. oX2d. o(X 1 3)X 22 22 723 21
Two scores, X and Y, are recorded for each of n 5 5 participants. For these scores, find the value of each expression.a. oXb. oYc. o(X 1 Y)d. oXY Subject X Y A 3 1 B 1 5 C 22 2 D 24 2 E 2 4
Use summation notation to express each of the following calculations:a. Add the scores and then square the sum.b. Square each score and then add the squared values.c. Subtract 2 points from each
For the following set of scores, find the value of each expression:a. oX2b. (oX)2c. o(X 2 3)d. o(X 2 3)2 X4 52 13
Use and create frequency distribution tables and explain how they are related to the original set of scores.
Calculate the following from a frequency table: oX, oX2, and the proportion and percentage of the group associated with each score.
Choose when it is useful to set up a grouped frequency distribution table, and use and create this type of table for a set of scores.
Describe how the three types of frequency distribution graphs—histograms, polygons, and bar graphs—are constructed and identify when each is used.
Use and create frequency distribution graphs and explain how they are related to the original set of scores.
Explain how frequency distribution graphs for populations differ from the graphs used for samples.
Identify the shape of a distribution—symmetrical, and positively or negatively skewed—based on a set of scores or a frequency distribution graph.
If the following scores are placed in a frequency distribution table, then what is the frequency value corresponding to X 5 2? Scores: 2, 3, 1, 1, 3, 3, 2, 4, 3, 1a. 1b. 2c. 3d. 4
For the following distribution of quiz scores, how many individuals took the quiz?a. 5b. 10c. 15d. 21
For the following frequency distribution, what is the value of oX2?a. 50b. 55c. 74d. 225
A set of scores ranges from a high of X 5 96 to a low of X 5 27.If these scores are placed in a grouped frequency distribution table with an interval width of 10 points, the top interval in the table
What is the lowest score in the following distribution?a. X 5 16b. X 5 17c. X 5 1d. cannot be determined
Which of the following statements is false regarding grouped frequency distribution tables?a. An interval width should be used that yields about 10 intervals.b. Intervals are listed in descending
Which of the following measuring scales are displayed by frequency distribution polygons?a. Either interval or ratio scalesb. Only ratio scalesc. Either nominal or ordinal scalesd. Only nominal scales
A group of quiz scores is shown in a histogram. If the bars in the histogram gradually decrease in height from left to right, what can you conclude about the set of quiz scores?a. There are more high

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