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essentials of statistics
Essentials Of Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau, Lori Ann B. Forzano - Solutions
Problem 9 presented data showing a positive relationship between weight and income for a sample of professional men. However, weight was coded in five categories that could be viewed as an ordinal scale rather than an interval or ratio scale. If so, a Spearman correlation is more appropriate than a
Problem 13 in Chapter 10 presented data demonstrating that handling money can reduce the perception of pain. In the study, one group counted money and another group counted blank pieces of paper. After the counting task, each participant dipped a hand into very hot water and rated how uncomfortable
Sketch a graph showing the line for the equation Y 5 2X 2 1.On the same graph, show the line for Y 5 2X 1 8.
A set of n 5 18 pairs of scores (X and Y values) has SSX 5 20, SSY 5 80, and SP 5 10.If the mean for the X values is MX 5 8 and the mean for the Y values is MY 5 10:a. Calculate the Pearson correlation for the scores.b. Find the regression equation for predicting Y from the X values.
A set of n 5 15 pairs of scores (X and Y values) produces a regression equation of Y⁄ 15 pairs of scores (5 2X 1 6.Find the predicted Y value for each of the following X scores:0, 2, 3, and 24.
For the following set of data, find the linear regression equation for predicting Y from X:X Y 2 1 7 10 5 8 3 0 3 4 4 13
For the following data:a. Find the regression equation for predicting Y from X.b. Calculate the Pearson correlation for these data.Use r 2and SSY to compute SSresidual and the standard error of estimate for the equation.X Y 3 3 6 9 5 8 4 3 7 10 5 9
For the following scores:X Y 3 8 5 8 2 6 2 3 4 6 1 4 4 7a. Find the regression equation for predicting Y from X.b. Calculate the predicted Y value for each X.
The regression equation is computed for a set of n 5 18 pairs of X and Y values with a correlation of r 5 10.50 and SSY 5 48.a. Find the standard error of estimate for the regression equation.b. How big would the standard error be if the sample size were n 5 66?
Solve the following problems.a. One set of 10 pairs of scores, X and Y values, produces a correlation of r 5 0.60. If SSY 5 200, find the standard error of estimate for the regression line.b. A second set of 10 pairs of X and Y values produces of correlation of r 5 0.40. If SSY 5 200, find the
Does the regression equation from Problem 20 account for a significant portion of the variance in the Y scores? Use a 5 .05 to evaluate the F-ratio.
Solve the following problems.a. A researcher computes the linear regression equation for a sample of n 5 20 pairs of scores, X and Y values. If an analysis of regression is used to test the significance of the equation, what are the df values for the F-ratio?b. A researcher evaluating the
De ne the distribution of sample means, describe the logically predictable characteristics of the distribution, and use this information to determine characteristics of the distribution of sample means for a speci c population and sample size.
Explain how the central limit theorem speci es the shape, central tendency, and variability for the distribution of sample means, and use this information to construct the distribution of sample means for a speci c sample size from a speci ed population.
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 standard error for samples of a speci c size selected from a speci ed population.
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 speci c 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 speci ed standard error or the new standard error produced by a speci c change in the sample size.
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 speci c sample suggests that a treatment effect is likely or is very unlikely.
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 for all of the sample means?a. 9b. 80c. 9(80) 5 720d. Cannot be determined without additional
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 from the same population and the mean is computed for each sample. How will the distribution of
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 sample means?a. The sample means tend to form a normal-shaped distribution.b. 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. 40d. 80
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 between M and m?a. 2 pointsb. 6 pointsc. 18 pointsd. Cannot be determined without additional information
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 1.00d. z 5 2.00
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. 0.0228
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. Increasing the sample size and decreasing the standard deviationd. Decreasing the sample size and increasing
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 obtain a standard error of less than 2 for any sized sample
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 scores with M 5 102c. A sample of n 5 25 scores with M 5 104d. A sample of n 5 100 scores with M 5
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 5 25d. M 5 84 for a sample of n 5 25
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 sample of n 5 25 scoresc. M 5 95 for a sample of n 5 9 scoresd. M 5 95 for a sample of n 5 25 scores
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 the sample has n 5 25 scores, what is the expected value of M and the standard error of M?
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 sample of n 5 4 scores from this population?b. On average, how much difference should there be for a
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 point
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 of n 5 4 scoresc. M 5 34 for a sample of n 5 16 scores
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 5 20c. If it was obtained from a population with m 5 60 and s 5 40
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 scoresb. M 5 91 for n 5 9 scoresc. M 5 91 for n 5 16 scoresd. M 5 91 for n 5 36 scores
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 the following?a. A sample of n 5 16 studentsb. A sample of n 5 25 studentsc. A sample of n 5 100
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 of n 5 4 scores with a mean less than M 5 51?c. What is the probability of selecting a sample of n
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 n 5 4?b. If the population distribution is positively skewed, what is the probability of obtaining a
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 middle 95% of the distribution of sample meansb. The range of sample means that defines the middle
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 sample of n 5 9 students with an average grade greater than 75? (Careful: This is a trick question.)b.
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 5 1.5, and forms a normal distribution. What is the probability of randomly picking a sample of n 5
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 25 scores
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 moderate alcohol consumption were shown photographs of females and asked to judge the attractiveness
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 typical, representative value or an extreme value for a sample of this size.a. M 5 64 for n 5 4
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 4 scores?b. Is this a representative sample mean or an extreme value for a sample
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 is a typical, representative value or an extreme value for each of the following:a. A population
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 de nitions are developed for constructs and identify the two components of an operational de nition.
Describe discrete and continuous variables and identify examples of each.
De ne 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 commercially prepared meals per week. For this study, the average of 2.3 meals is an example of a .a.
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. sampleb. statisticc. populationd. parameter
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. descriptive statisticsd. inferential statistics
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 their average score?a. 500b. greater than 500c. less than 500d. around 500 but probably not equal to
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. None of the above.
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 variables and one groupd. Two variables and two groups
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, Demers, & Wechsler, 2002).What research design did this study use?a. Correlationalb. Experimentalc.
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 the independent variable?a. The rats given the genetically modi ed dietb. The rats given the
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 of steps in a summation problem
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 individual sends each day, and calculates the average number for the group.a. Identify the population for
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 used and identify whether the variable is continuous or discrete.
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 obtained from measurements on an ordinal scale compared to measurements on a nominal scale?b. What
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 2% milk(Scharf, Demmer, & DeBoer, 2013). Is this an example of an experimental or a nonexperimental
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 experienced more video game violence were also more hostile and had more frequent arguments with teachers.
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 neutral words. Identify the independent and dependent variables for this study.
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 students were then given a test on the material and the researchers recorded the number of correct
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 students a color photograph of a 24-year-old woman with a tattoo of a dragon on her arm. A second group
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 customers gave significantly bigger tips to waitresses when they were wearing red. For this study, identify
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 score and then add the resulting values.d. Subtract 1 point from each score and square the resulting
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.
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