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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Refer to Exercise 15.31. Suppose that 600 registered voters had been surveyed both before and after the debate and that the observed data were Use McNemar’s Test to determine if the proportion of all registered voters who prefer X decreased after the debate.Give a p-value and state a conclusion.
Suppose that 400 registered voters are surveyed about which of two candidates (X and Y) for a political office they prefer both before and after a televised debate between the candidates. The following table summarizes preferences both before and after the debate
In an activity in a statistics class, students were asked if they had ever been pulled over by a police officer while driving.The following table summarizes results, as counts, classified by sex.
Explain how sample size affects the statistical significance of a fixed amount of difference between two sample proportions.
Weindling et al. (1986; also in Hand et al., 1994, p. 15) were interested in the health of juvenile delinquents. They classified 16 boys who failed a vision test by whether or not they wore glasses and whether or not they were a juvenile delinquent.They were interested in knowing whether the
Refer to Exercise 15.26. In each case, specify the null and alternative hypotheses.
In each of the following situations, explain which test would be most appropriate: a chi-square test, a one-sided z-test for the difference in two proportions, or a Fisher’s Exact Test.a. The manufacturer of a safety seal that is used in cars wants to know whether the safety seals perform as well
The use of magnets has been proposed as a cure for various illnesses. Suppose that researchers conduct a study with ten participants to determine whether using magnets as therapy reduces pain from migraine headaches. Five participants are randomly assigned to receive the magnet treatment, and of
Refer to Exercise 15.12, in which the relationship between sex (male, female) and seatbelt use was examined.a. Compute the chi-square statistic using the shortcut formula given in Section 15.2. Show your work.b. What are the degrees of freedom for this situation?c. Find the p-value or p-value range
about age and opinion on gambling.Would a z-test for the difference in two proportions have been appropriate instead of a chi-square test? If your answer is yes, explain whether the results would have been identical to the results of the chi-square test. If your answer is no, explain why not.
about height and the risk of having been bullied for secondary school students. Use the shortcut formula to calculate the value of the chi-square statistic for those data.
The data in the table below first appeared in Exercise 4.11.The variables are height (short or not) and whether or not the student had ever been bullied in school for 209 secondary school students in England. The researchers gathered the data to test their hypothesis that short students are more
about sex (male, female) and type of statistics class students were taking. Use the shortcut formula to calculate the value of the chi-square statistic for those data.
Refer to the data given for Exercise 15.11. about opinion on the death penalty and opinion on the legalization of marijuana. Use the shortcut formula to calculate the value of the chi-square statistic for those data.
The data for this exercise were first given in Table 4.3 for Example 4.2. The following table classifies Australian couples who were married at the beginning of a 3-year study by the smoking habits of the couple and whether the couple separated or not during the study period. The table gives counts
The following table was first given in Exercise 4.4 in Chapter 4. It contains counts and row percentages for data on age group and frequency of reading newspapers for respondents in the 2008 General Social Survey
The following drawing illustrates the water-level task.Several developmental psychologists have investigated performance on this task. The figure on the left shows the water level in a glass of water that is half full (or is it half empty?).The figure on the right shows the same glass tipped to the
In Exercise 2.30 data were presented on seatbelt use and grades for a sample of 2530 twelfth-graders, collected as part of the 2001 Youth Risk Behavior Surveillance System.Students were asked how often they wear a seatbelt while driving; possible choices were never, rarely, sometimes, most times,
An article on the Gallup website titled “SOCIAL AUDIT, Gambling in America” included the following comparison of the responses of teenagers and adults to the question,“Generally speaking, do you approve or disapprove of legal gambling or betting?” The survey was conducted in April 1999.
(p. 587) for xylitol and ear infection data, verify that the null hypothesis“expected” proportion getting an ear infection is the same for the three treatment groups.
For the expected counts shown in Table
The data for this exercise are from a sample of twelfthgraders, collected as part of the 2001 Youth Risk Behavior Surveillance System. The students were asked how often they wear a seatbelt while driving, and for this exercise, we combine the responses for “never” and “rarely” and
In the 2008 General Social Survey conducted by the National Opinion Research Center at the University of Chicago, participants were asked:Do you favor or oppose the death penalty for persons convicted of murder?Do you think the use of marijuana should be made legal or not?A two-way table of counts
Suppose that investigators conduct a study on the relationship between birth order (first or only child, not first or only child) and activity preference (indoor or outdoor).a. Write null and alternative hypotheses for the two variables in this situation.b. Suppose that the p-value of the study is
◆ Students from two different statistics classes at UC Davis reported their sex (male, female) and recorded which class they were taking. One class is for liberal arts students, and the other is for non–liberal arts students. The results for the 173 students are given below. In each cell, the
Refer to Exercise 15.6. For each part, determine whether the result is statistically significant at the .01 level of significance.
Recall that the critical value for a chi-square test is the chisquare value for which the area to its right equals the level of significance. Use Table A.5 to determine the critical value in each of the following situations.a. Level of significance is a 5 .05; df 5 1.b. Level of significance is a 5
For each of the following situations, determine whether the result is statistically significant at the .05 level of significance.a. x2 5 2.89, df 5 1.b. x2 5 5.00, df 5 1.c. x2 5 23.60, df 5 4.d. x2 5 23.60, df 5 15.
for a table with 2 rows and 3 columns.d. x2 5 2.28, df 5 9.
In each of the following situations, give the p-value for the given chi-square statistic. Either use the information in Table A.5 to provide a range for the p-value or use software to determine an exact value.a. x2 5 3.84, df 5 1.b. x2 5 6.7 for a table with 3 rows and 3 columns.c. x2 5
Sex (female or male) and handedness (right-handed or lefthanded) are recorded for a randomly selected sample of adults. Of the 100 women in the sample, 92 women are right-handed. Of the 80 men in the sample, 70 men are right-handed.a. Write a two-way table of observed counts.b. Determine expected
In a nationwide survey, college students are asked how important religion is in their life (very, fairly, or not very)and whether they have ever cheated on a college exam (no or yes).a. Write null and alternative hypotheses about the two variables in this situation. Make your hypotheses specific to
For each pair of variables, indicate whether a two-way table would be appropriate for summarizing the relationship. In each case, briefly explain why or why not.a. Sex (female, male) and amount willing to spend on a home theater system.b. Age group (under 20, 21–29, etc.) and handedness
For each pair of variables, indicate whether a two-way table would be appropriate for summarizing the relationship. In each case, briefly explain why or why not.a. Satisfaction with quality of local K through 12 schools(satisfied or not satisfied) and political party (Republican, Democrat, etc.).b.
about the relationship between height(height) and foot length (foot) for the dataset heightfoot.a. Do not omit any outliers. Use the complete dataset to determine a 90% prediction interval for the height of a man whose foot length is 28 cm.b. Explain why the interval computed in part (a) is wider
Use the dataset heightfoot from the companion website for this exercise. Heights (inches) and foot lengths (centimeters) are given for 33 men.a. Plot y 5 height (height) versus x 5 foot length (foot).What important features are evident in the plot?
Use the bears-female dataset from the companion website for this exercise. Weights (pounds) and chest girths (inches)are given for n 5 19 female wild bears. The corresponding variable names are Weight and Chest.a. Plot y 5 Weight versus x 5 Chest. Describe the important features of the plot.b.
Refer to the previous exercise about letters written with the dominant (y) and nondominant (x) hands.a. Plot residuals versus x 5 nondom. What does this plot indicate about conditions for using the linear regression model?
Use the dataset letters from the companion website for this exercise. A sample of 63 students wrote as many capital letters of the alphabet in order as they could in 15 seconds using their dominant hand, and then they repeated this task using their nondominant hand. The variables dom and nondom
Explain why rejecting H0: b1 5 0 in a simple linear regression model does not prove that the relationship is linear. To answer this question, you might find it helpful to consider the figure in Exercise 14.46, which shows stopping distance and vehicle speed for automobiles.
The five steps for hypothesis testing were given in Chapters 12 and 13. Describe those steps as they apply to testing whether there is a relationship between two variables in the simple linear regression model.
appears to be violated?What corrective action(s) should you consider?
and 14.55. The output provides prediction intervals and confidence intervals for father’s heights of 65, 70, and 74 inches.a. Verify that the “Fit” given by Minitab for father’s height of 65 inches is consistent with the predicted height that would be given by the regression equation.b.
Refer to Exercise 14.54.a. What is the value of R2 for the observed linear relationship between height and father’s height? Write a sentence that interprets this value.b. What is the value of the correlation coefficient r?
◆ This exercise refers to the following Minitab output, relating y 5 son’s height to x 5 father’s height for a sample of n 5 76 college males. (Note: The data are in the dataset UCDavis1 on the companion website.)
The following data are x 5 average on five quizzes before the midterm exam and y 5 score on the midterm exam for n 5 11 students randomly selected from a multiple-section statistics class of about 950 students:a. Plot the data, and describe the important features of this plot.b. Using statistical
Exercise 14.47. gave linear regression results for the relationship between y 5 hours of sleep the previous day and x 5 hours spent studying the previous day. Following is Minitab output showing a confidence interval and a prediction interval for hours of sleep when hours of studying 5 3 hours:
are verified by this plot
Regression results for the relationship between y 5 hours of sleep the previous day and x 5 hours spent studying the previous day were given in Exercise 14.47. The figure for this exercise is a plot of residuals versus hours spent studying. What does the plot indicate about the necessary conditions
about hours of sleep and hours of study.a. What is the value of the standard deviation from the regression line? Write a sentence that interprets this value.b. Calculate the predicted value of hours of sleep the previous day for a student who studied 4 hours the previous day.c. Using the Empirical
Data for y 5 hours of sleep the previous day and x hours of studying the previous day for n 5 116 college students were shown in Figure 3.14 (p. 85) and described in Example 3.15. Some regression results for those data are as follows:
The figure for this exercise shows data for the relationship between the average stopping distance (feet) of a car when the brakes are applied and vehicle speed (miles per hour).The regression line for these data is also shown on the plot.(Note: The raw data were given in Exercise 3.7.)a. Which one
◆ Observed data along with the sample regression line for the relationship between body weight (pounds) and neck girth (inches) for 19 female bears of various ages are shown in the figure below. (Note: The data are in the dataset bearsfemale on the companion website.)a. Which one of the necessary
The figure accompanying this exercise is a histogram of the residuals for a simple linear regression. What does this plot indicate about the necessary conditions for conducting a linear regression? Be specific about which of the five necessary conditions are verified in this figure.
◆ The figure for this exercise is a histogram of the residuals for a linear regression relating y 5 height (inches) and x 5 foot length (centimeter) for a sample of college men.Discuss what the histogram indicates about Conditions 2(no outliers) and 4 (normality) for linear regression listed at
about a linear regression for y 5 pulse after marching in place and x 5 pulse before marching in place. The figure for this exercise is a plot of residuals versus the pulse before marching for a sample of 40 students. Discuss what the plot indicates about Conditions 1, 2, and 3 for linear
that should be at least approximately true for linear regression. Which of the conditions can be checked by using each of the following methods? In each case, list all of the conditions that can be checked.a. Drawing a histogram of the residuals.b. Drawing a scatterplot of the residuals versus the
There are five conditions listed at the beginning of Section
Suppose that a linear regression analysis of the relationship between y 5 systolic blood pressure and x 5 age is done for women between 40 and 60 years old. For women who are 45 years old, a 90% confidence interval for E(Y) is determined to be 128.2 to 131.3. Explain why it is incorrect to conclude
Refer to Exercise 14.37. Using the general format for a 95%confidence interval, verify the confidence interval for the mean given by Minitab. Note that the standard error of the“Fit” is given.
Refer to Exercise 14.37, giving the relationship between husbands’ and wives’ ages for a sample of British couples.a. Interpret the “95% CI” given by Minitab. Be specific about what the interval estimates.b. Interpret the “95% PI” given by Minitab. Be specific about what the interval
Example 2.17 (p. 47) described the heights of a sample of married British women. The ages of the women and their husbands were available in the same dataset for n 5 170 couples. For the sample, the linear regression line relating y 5 husband’s age and x 5 wife’s age is y^ 5 3.59 1 0.9667x.The
◆ The dataset oldfaithful on the companion website provides data collected on 299 eruptions of the Old Faithful geyser in Yellowstone Park. The variables are x 5 duration of the eruption (in minutes) and y 5 time until the next time the geyser erupts (in minutes). The following Minitab output
1 0.894x, where y 5 pulse after marching and x 5 pulse before marching. The following Minitab output gives a confidence interval and a prediction interval for pulse after marching when pulse before marching is 70.(Data source: pulsemarch dataset on the companion website.)
◆ Forty students measure their resting pulse rates, then march in place for 1 minute and measure their pulse rates after the marching. The regression line for the sample is y^ 5
A college finds that among students who had a total SAT score of approximately 1200, about 90% have a first-year GPA in the range 2.7 to 3.7. Is this interval a prediction interval or a confidence interval for the mean? Explain.
Suppose a regression model is used to analyze the relationship between y 5 grade point average and x 5 number of classes missed in a typical week for college students.a. In the context of this situation, explain what would be predicted by a prediction interval for y when x 5 2 classes missed per
For each of the following two situations, explain whether it would be more appropriate to use a confidence interval for the mean or a prediction interval for a value of y.a. Estimate the average income for individuals who have 20 years of experience within a particular occupation.b. Estimate the
For each of the following two situations, explain whether it would be more appropriate to use a confidence interval for the mean or a prediction interval for a value of y.a. Estimate the first-year college GPA for a student whose high school GPA was 3.5.b. Estimate the mean first-year college GPA
Refer to Exercise 14.29, in which correlations were given for the relationship between hours of watching music videos and both perceived appearance and weight concerns. The correlations were based on data from 837 ninth-grade girls.a. Do the correlation values given by the researchers indicate weak
A sample of 837 ninth-grade girls was asked how much time they spent watching music videos each week. The girls also were asked to rate how concerned they were about their weight on a scale of 0 to 100 (100 5 extremely concerned) as well as to rate their perception of how important appearance is on
as 0.0042. Calculate an approximate 95% confidence interval for the slope in the population. Write a sentence that interprets this interval.c. Use your answer in part (b) to find an approximate 95% confidence interval for the predicted decrease in body temperature as someone ages by 10 years.
2 0.0138(Age).a. The slope of the line is 20.0138. Explain whether the proper notation for this slope is b1 or b1.b. The standard error for the slope was given in the output accompanying Exercise
the regression relationship between age and body temperature based on 100 blood donors was given as Temperature 5
(p. 555), a sample of n 5 43 college men was used to determine the regression equation, Weight 5 2318 1 7(Height). Weights were measured in pounds and heights were measured in inches.a. The slope of the line is 7. Is the proper notation for this slope b1 or b1? Explain.b. The standard error for the
The relationship between y 5 hours of watching television in a typical day and x 5 age was examined in Example 3.14.The data were gathered in the 2008 General Social Survey done by the National Opinion Research Center at the University of Chicago, and there were n 5 1288 observations. The
◆ This output is for a linear regression relating y 5 GPA and x 5 hours per week spent using the computer for n 5 162 college students. The data are in the UCDavis1 dataset on the companion website. Note that 11 of the 173 students surveyed did not provide complete data.
for the simple linear regression with y 5 body temperature and x 5 age.a. Write null and alternative hypotheses for testing whether there is a linear relationship between body temperature and age. Use proper statistical notation.b. Use information given in the output to test the hypotheses written
for the simple linear regression with y 5 average April temperature and x 5 geographic latitude for 20 U.S. cities.a. Write null and alternative hypotheses for testing whether there is a linear relationship between mean April temperature and latitude. Use proper statistical notation.b. Use
Refer to the output given in Exercise
For men over the age of 40, a linear regression is done to examine the relationship between y 5 systolic blood pressure and x 5 age. A 95% confidence interval for the population slope b1 is 0.3 to 0.7. In the context of this situation, write a sentence that interprets this confidence interval.
◆ The UCDavis1 dataset on the companion website includes grade point averages and self-reported hours per week of watching television for students in a statistics class.In a simple linear regression for the relationship between y 5 grade point average and x 5 hours per week of television
in which results are given for the relationship between y 5 body temperature and x 5 age. The analysis of variance table for this relationship is as follows:
(p. 557) for guidance.a. SSTO.b. SSE.c. r2.
and 14.13. in which results are given for the relationship between y 5 mean April temperature and x 5 geographic latitude for 20 U.S. cities. The analysis of variance table for this relationship is as follows:Find or compute the following values based on this information. Refer to Example
Refer to Exercises
Sketch sample data for which the standard deviation from the regression line is s 5 0.
The least-squares regression line is y^ 5 9 1 2x for these six observations of x and y:x 113355 y 10 12 13 17 17 21a. For each observation, calculate the residual. Verify that the sum of the residuals is 0.b. Compute SSE, the sum of squared errors (residuals).c. For the sample, calculate the
degrees? Justify your answer.
degrees. Compute the residual for each of these individuals.c. The standard deviation from the regression line in this example is approximately s 5 0.70 degrees. Use the Empirical Rule to give an interval that describes body temperature for about 95% of the population of people who are 21 years
2 0.0138(Age).a. What is the predicted body temperature for someone who is 21 years old?b. There were two individuals in the sample who were 21 years old. Their body temperatures were
Refer to Exercise 14.14, in which the regression relationship between y 5 body temperature and x 5 age was given in Minitab output as y^ 5
(p. 557) gave the regression equation y^ 5 577 2 3.01x for the relationship between y 5 maximum distance at which a driver can read a highway sign and x 5 driver age. The data are in the dataset signdist on the companion website.a. What is the predicted value of the maximum sign-reading distance
◆ The dataset bodytemp on the companion website gives age in years and body temperature in degrees Fahrenheit for 100 blood donors ranging in age from 17 to 84 years old.Minitab output for the linear regression is as follows:
Refer to Exercise 14.1. about mean April temperatures and geographic latitudes for U.S. cities. Minitab output for the linear regression is as follows:
described the relationship between y 5 handspan (centimeters) and x 5 height(inches). The sample consisted of measurements of both variables for n 5 167 college students, available in the dataset handheight on the companion website. Computer output for this example is as followsa. What is the value
◆ An example in Section
Find r2 in each of the following situations:a. SSTO 5 500, SSE 5 300.b. SSTO 5 200, SSE 5 40.c. SSTO 5 80, SSE 5 0.d. SSTO 5 100, SSE 5 95.
In the simple linear regression model for a population, the relationship between the x variable and the mean of the y variable is E(Y) 5 b0 1 b1x.a. Suppose b1 5 0. What would be the appearance of this line? Draw a sketch illustrating your answer.b. Explain how the answer to part (a) illustrates
Suppose that the population regression equation relating y 5 weight (pounds) and x 5 height (inches) for men aged 18 to 29 years old is Mean weight 5 2250 1 6(Height).An individual in this population is 70 inches tall and weighs 180 pounds. Give numerical values for each of the following for this

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