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a course in statistics with r
Mind On Statistics 5th Edition Jessica M Utts, Robert F Heckard - Solutions
16.2 In each situation, determine whether one-way analysis of variance could be an appropriate method for analyzing the data described. Briefly explain why or why not for each part.a. A psychiatrist compares four treatment programs for clinical depression. The response variable is whether or not a
16.1 In each situation, determine whether one-way analysis of variance could be an appropriate method for analyzing the data described. Briefly explain why or why not for each part.a. A researcher compares the mean blood pressures of men over 50 years old for three different ethnic groups. He
15.71 Use the Student2010 dataset. The variable LiveWhere indicates whether a student lives in a dorm or off-campus. The variable AlcMissClass indicates whether a student has ever missed a class due to drinking alcohol.a. Create a two-way table that summarizes the relationship between LiveWhere and
15.70 This is also Exercise 4.84 (slightly modified). Use the Student2010 dataset. The variable UseCell gives student responses to a question that asked students how they mainly used a cell phone (to talk, to text).a. Create a two-way table that summarizes the relationship between Sex and
15.69 For this exercise, use the UCDavis2 dataset. Identify two variables for which it would be of interest to you to test whether there is a relationship. Carry out the five steps of the chi-square test. If one or both of the variables are quantitative, create reasonable categories. For instance,
15.68 For this exercise, use the UCDavis2 dataset. Two variables that were measured were whether the respondent was leftor right-handed (Hand) and whether the respondent finds it easier to make friends with people of the same or opposite sex (Friends). Carry out the five steps to determine whether
15.67 For this exercise, use the UCDavis2 dataset. Respondents were categorized as male or female (Sex) and were asked whether they typically sit in the front, middle, or back of the classroom (Seat).a. Carry out the five steps to determine whether there is a significant relationship between these
15.66 For this exercise, use the GSS-08 dataset on the companion website. The variable owngun indicates whether or not the respondent owns a gun, and the variable polparty contains the respondent’s political party preference. Is there a significant relationship between owngun and polparty?a.
15.65 Gillespie (1999) and Chambers (2000) reported on two Gallup polls, taken in August 1999 and August 2000 using independent samples, which asked parents the question, “How satisfied are you with the quality of education your oldest child is receiving? Would you say completely satisfied,
15.64 Refer to Exercise 15.63. Using the original data (not combining green and hazel), construct a contingency table for the two variables:Explanatory variable: Eye color.Response variable: Finds own eye color most attractive, yes or no.a. Conduct a chi-square test to determine if these two
15.63 Students (n 5 183) were asked to identify their own eye color as well as the eye color to which they are most attracted.The results are shown here:Eye Color and Attraction Eyes Attracted To Own Eyes Brown Blue Hazel Green Total Brown 30 22 6 13 71 Blue 15 37 3 11 66 Hazel 4 12 7 7 30 Green 4
15.62 Explain why a chi-square test statistic cannot be negative.
15.61 Refer to Exercise 15.60. Suppose that the same question were to be asked in many independent surveys. Assuming that the null hypothesis is true, into what range should the test statistic fall about 95% of the time, where 0 is at the lower end of the range?
15.60 In the 2008 General Social Survey, participants were asked,“Should divorce in this country be easier or more difficult to obtain than it is now?” The results are shown in the following table and Minitab output.Sex Easier More Difficult Stay Same Total Male 165 278 159 602 Female 199 331
15.59 In a class survey, statistics students were asked, “Which one of these choices describes your perception of your weight:about right, overweight, or underweight?” The table in Exercise 4.12 displayed the results by sex. Displayed below are those results along with the Minitab output for a
15.58 Wilding and Cook (2000) asked 352 males and 376 females to listen to a male voice and a female voice. One week later, they attempted to identify the voices they had heard in lineups of six male and six female voices. The results are shown in the following table. Using appropriate subsets of
15.57 Refer to Exercise 15.56. Use the shortcut formula for 2 3 2 tables to compute the chi-square statistic. Show the formula with all numbers entered.
15.56 Case Study 10.3 (p. 399) described a survey in which students in a statistics class were asked, “Would you date someone with a great personality even though you did not find them attractive?” The results were that 80 of 131 women answered “yes” and 26 of 61 men answered “yes.”a.
15.55 Household sizes for the households participating in the 1996 General Social Survey conducted by the National Opinion Research Center at the University of Chicago are shown in the following table. The table also shows the proportion of households of each size in the survey and the
15.54 Refer to Exercise 15.51, in which each student guessed the results of ten coin flips. If all students are just guessing, and if the coins are fair, then the number of correct guesses for each student should follow a binomial distribution.a. What are the parameters n and p for the binomial
15.53 The data in this exercise were first presented in Exercise 4.8. In the 2008 General Social Survey, religious preference and opinion about when premarital sex is wrong were among the measured variables. The contingency table of counts for these variables is shown in Exercise 4.8 and again
15.52 In a study reported in the Annals of Internal Medicine (Lotufo et al., 2000), the investigators examined the possible relationship in men between baldness and the risk of coronary heart disease. Other researchers have reported a possible link between these two variables (see Case Study 6.4,
15.51 Example 15.12 (p. 612) described an experiment in which students were classified as “Sheep” who believe in ESP or as“Goats” who do not. Each student then guessed the results of ten coin tosses. We classify students as “Stars” if they guessed five or more correctly and as
15.50 Refer to Exercise 15.47. Note that the “contributions to chi-square” are given in the output for all cells. For instance, the “contribution to chi-square” for the row “18–29” and the column “Very” is 0.175, and for the row “18–29” and the column “Not at All” it is
15.49 Exercise 4.63 gave data on ear piercings and tattoos for a sample of 1375 college women. The data are presented again in the following table. The piercings response is the total number of ear piercings for a woman, and this has been categorized.Ear Piercings and Tattoos, 1375 College Women
15.48 Answer Thought Question 15.1 on page 606.
15.4 illustrating where the calculated chi-square statistic falls relative to values in Table A.5.f. Refer to the output below. What is the expected count for the “501, Not Too Satisfied” cell? Show how to calculate this expected count.Expected counts are printed below observed counts Very
15.47 In a survey reported in a special issue of Newsweek magazine(Special Edition: Health for Life, Spring/Summer 1999), n 5 747 randomly selected women were asked,“How satisfied are you with your overall appearance?”There were four possible responses to this question, and the following table
15.46 In a 2012 survey of Internet users done by the Pew Center, respondents were asked whether they used social networking sites. The following 3 × 2 table of counts and row percentages displays the results by age of the respondent:Use Social Networking Sites?Age Yes No Total 18-29 264 (83%) 54
15.45 In CBS News polls conducted in 2001, 2004, and 2010, respondents were asked whether they favor or oppose mandatory testing of students in public schools each year to determine how well the school is educating students.The following 3 × 3 table of counts was estimated from percentages
15.44 The California Daily 3 lottery game is identical to the Pennsylvania Daily Number game described in Example 15.15 (p. 618). The following table contains the observed distribution of all digits drawn in the California Daily 3 on the 200 days between May 14, 2000, and November 29, 2000.Three
15.43 One of the authors of this book purchased four 1-pound bags of plain M&Ms at different stores in Pennsylvania to compare the color distribution to the one stated on the manufacturer’s website in 2000. The observed results for the combined bags and the proportions alleged by the manufacturer
15.42 The following table contains the observed distribution of the last digit of the forecasted high temperature on December 10, 2000, for n 5 150 U.S. and international cities. (Source:New York Times, December 10, 2000, p. 47.)Last Digit 0 1 2 3 4 5 6 7 8 9 Count 11 21 11 23 10 17 11 15 13 18a.
15.41 Refer to Exercise 15.40. Suppose that a car manufacturer had hypothesized that 50% would prefer silver, 30% would prefer blue, and 20% would prefer green. Test the manufacturer’s hypothesis. Use a 5 .05.
15.40 In a class survey done in a statistics class, students were asked, “Suppose that you are buying a new car and the model you are buying is available in three colors: silver, blue, or green. Which color would you pick?” Of the n 5 111 students who responded, 59 picked silver, 27 picked
15.39 Suppose that a statistics teacher assigns her class of 60 students the homework task of flipping a coin two times, counting the number of heads, and submitting that number to her during the next class period.a. List the possible sequences of results for two flips of a coin.Using this list,
15.38 Suppose that on a typical day, the proportion of students who drive to campus is .30 (30%), the proportion who bike is.60 (60%), and the remaining .10 (10%) come to campus in some other way (e.g., walk, take the bus, get a ride). The campus sponsors a “spare the air” day to encourage
15.37 The following table shows the results from 190 students“randomly” choosing among the integers from 1 to 10. For example, there were two students who chose the digit 1 and nine students who chose the digit 2. (Raw data are in the pennstate1 dataset on the companion website.)Digit 1 2 3 4 5
15.36 In a chi-square goodness-of-fit test, is it possible for all of the expected counts to be larger than the corresponding observed counts? Explain.
15.35 Explain whether each of these is possible in a chi-square goodness-of-fit test.a. The chi-square statistic is negative.b. The chi-square statistic is 0.c. The expected counts are not whole numbers.d. The observed counts are not whole numbers.e. The probabilities specified in the null
15.34 In the following situations, give the expected count for each of the k categories.a. k 5 4, H0: p1 5 .2, p2 5 .4, p3 5 .1, p4 5 .3, and n 5 2000.b. k 5 5, H0: all pi are the same, and n 5 2500.
15.33 In the following situations, give the expected count for each of the k categories.a. k 5 3, H0: p1 5 p2 5 p3 5 1/3, and n 5 300.b. k 5 3, H0: p1 5 1/4, p2 5 1/4, p3 5 1/2, and n 5 1000.
15.32 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 Number of Voters Preferred X before and after 300 Preferred Y before and after 265 Preferred X before, Y after 25 Preferred Y before, X after 10 Use
15.31 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.Number of Voters Preferred X
15.30 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
15.29 Refer to Exercise 15.28. In each case, specify the null and alternative hypotheses.
15.28 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
15.27 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
15.26 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
15.25 Refer to Exercise 15.14 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
15.24 Refer to the data given for Exercise 15.23 about height and the risk of having been bullied for secondary school students.Use the shortcut formula to calculate the value of the chisquare statistic for those data.
15.23 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
15.22 Refer to the data given for Exercise 15.9 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.
15.21 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 chisquare statistic for those data.
15.20 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.Ever Pulled Over by an Officer?Sex No Yes Total Male 7 15 22 Female 16 18 34 Total 23 33 56a.
15.19 Explain how sample size affects the statistical significance of a fixed amount of difference between two sample proportions.
15.18 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
15.17 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.Frequency of Reading Newspapers Age Group Every Day A Few Times a Week Once a
15.16 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
15.15 In Exercise 2.30 data were presented on seatbelt use and grades for a sample of 2530 twelfth-graders, collected as part 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
15.14 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
15.13 For the expected counts shown in Table 15.3 (p. 603) 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.
15.12 The data for this exercise are from a sample of twelfth-graders, 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
15.11 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
15.10 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. Make sure you specify the population
15.9 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
15.8 Refer to Exercise 15.6. For each part, determine whether the result is statistically significant at the .01 level of significance.General Section Exercises
15.7 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
15.6 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.
15.5 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 26.23
15.4 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
15.3 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
15.2 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
15.1 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,
14.63 Refer to Exercise 14.62 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
14.62 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?b. Omit any outliers evident in the plot in
14.61 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
14.60 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?b. Create a histogram of the residuals. What does this plot indicate
14.59 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
14.58 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.Dataset Exercises
14.57 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.
14.56 Refer to Exercises 14.54 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
14.55 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?
14.54 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 regression equation is Height 5 30.0 1 0.576 dadheight 76 cases used, 3
14.53 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:x 5 Quizzes 80 68 94 72 74 83 56 68 65 75 88 y 5 Exam 72 71 96 77 82 72 58 83 78 80
14.52 Refer to the output given in Exercise 14.12 about handspan and height. Compute a 90% confidence interval for the population slope. Write a sentence that interprets this interval.
14.51 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
14.50 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
14.49 Refer to Exercises 14.47 and 14.48 about hours of sleep and hours spent studying. What is the intercept of the regression line? Does this value have a useful interpretation in the context of this problem? If so, what is the interpretation? If not, why not?
14.48 Refer to Exercise 14.47 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
14.47 Data for y 5 hours of sleep the previous day and x 5 hours of studying the previous day for n 5 116 college students were shown in Figure 3.14 (p. 86) and described in Example 3.15. Some regression results for those data are as follows:The regression equation is Sleep 5 7.56 2 0.269 Study
14.46 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
14.45 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
14.44 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.–4 –3
14.43 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
14.42 Refer to Exercise 14.35 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,
14.41 There are five conditions listed at the beginning of Section 14.5 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
14.40 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
14.39 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.
14.38 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
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