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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
10.87 Parental support and household type A recent study interviewed youths with a battery of questions that provides a summary measure of perceived parental support.This measure had sample means of 46 1s = 92 for the single-mother households and 42 1s = 102 for the households with both biological
10.85 Sex roles A study of the effect of the gender of the tester on sex-role differentiation scores13 in Manhattan gave a random sample of preschool children the Occupational Preference Test. Children were asked to give three choices of what they wanted to be when they grew up. Each occupation was
10.84 Test—CI connection In the previous exercise, explain how the result of the 95% confidence interval in part b corresponds to the result of the decision using significance level 0.05 in part c.
10.82 Ibuprofen and lifespan Geneticists hypothesized that one reason for a prolonged lifespan observed in yeast cells treated with the common drug ibuprofen stems from inhibiting the uptake of certain amino acids. In an experiment, they compared levels of amino acids in cells treated with
10.81 Test TV watching by race Refer to the previous exercise.a. Specify the hypotheses that are tested in the output shown.b. Report the value of the test statistic and the P-value.Interpret.c. Make a decision, using the 0.05 significance level.d. Explain the connection between the result of this
10.78 Females or males have more close friends? A recent GSS reported that the 486 surveyed females had a mean of 8.3 close friends 1s = 15.62 and the 354 surveyed males had a mean of 8.9 close friends 1s = 15.52.a. Estimate the difference between the population means for males and females.b. The
10.77 Belief depend on gender? Refer to the previous exercise.a. Find the standard error of 1pn 1 - pn 22 for a test of H0: p1 = p2.b. For a two-sided test, find the test statistic and P-value and make a decision using significance level 0.05.Interpret.c. Suppose that actually p1 = 0.81 and p2 =
10.76 Gender and belief in afterlife The table shows results from the 2014 General Social Survey on gender and whether one believes in an afterlife.Belief in Afterlife Gender Yes No Total Female 1026 207 1233 Male 757 252 1009a. Denote the population proportion who believe in an afterlife by p1 for
10.75 Marijuana and gender In a survey conducted by Wright State University, senior high school students were asked if they had ever used marijuana. The table shows results of one analysis, where X is the count who said yes. Assuming these observations can be treated as a random sample from a
10.74 BMI then and now The Centers for Disease Control(www.cdc.gov) periodically administers large randomized surveys to track health of Americans. In a survey of 4431 adults in 2003/2004, 66% were overweight (body mass index BMI Ú 25). In the most recently available survey of 5181 adults in
10.73 Public versus scientists’ opinions on fracking A Pew Research Center survey of 2002 U.S. adults in August 2014 and a survey of 3748 scientists connected to the American Association for the Advancement of Science(AAAS) in September 2014 both asked the following question: "Do you favor or
10.72 Pick the method Steve Solomon, the owner of Leonardo’s Italian restaurant, wonders whether a redesigned menu will increase, on the average, the amount that customers spend in the restaurant. For the following scenarios, pick a statistical method from this chapter that would be appropriate
10.71 Breast cancer over time The percentage of women who get breast cancer sometime during their lifetime is higher now than in 1900. Suppose that breast cancer incidence tends to increase with age, and suppose that women tend to live longer now than in 1900. Explain why a comparison of breast
10.70 Heart disease and age In the United States, the median age of residents is lowest in Utah. At each age level, the death rate from heart disease is higher in Utah than in Colorado. Overall, the death rate from heart disease is lower in Utah than Colorado. Are there any contradictions here, or
10.66 Death penalty in Kentucky A study of the death penalty in Kentucky reported the results shown in the table. (Source:Data from T. Keil and G. Vito, Amer. J. Criminal Justice, vol. 20, 1995, pp. 17–36.)a. Find and compare the percentage of white defendants with the percentage of black
10.65 Benefits of drinking A USA Today story (May 22, 2010) about the medical benefits of moderate drinking of alcohol stated that a major French study links those who drink moderately to a lower risk for cardiovascular disease but challenges the idea that moderate drinking is the cause.
10.64 Marital status and life insurance by age Refer to the previous exercise. Results in this poll also depended strongly on the age of the respondents. For instance, the percentages of respondents (married, having a life insurance policy) were (10%, 5%) between the ages of 18 to 24 years, (45%,
10.63 Marital status and life insurance Adult males participating in a poll were asked whether they were married and whether they had subscribed to a life insurance policy. Of all the respondents, 42% males said that they were married and 32.6% said that they had a life insurance policy.a. Estimate
10.62 President’s popularity Last month a random sample of 1000 subjects was interviewed and asked whether they thought the president was doing a good job. This month the same subjects were asked this again. The results are:450 said yes each time, 450 said no each time, 60 said yes on the first
10.60 Treat juveniles as adults? The table that follows refers to a sample of juveniles convicted of a felony in Florida.Matched pairs were formed using criteria such as age and the number of prior offenses. For each pair, one subject was handled in the juvenile court and the other was transferred
10.59 Comparing speech recognition systems Table 10.20 in Example 17, repeated here, showed results of an experiment comparing the results of two speech recognition systems, GMDS and CDHMM.CDHMM GMDS Correct Incorrect Correct 1921 58 Incorrect 16 5a. Estimate the population proportion p1 of correct
10.58 Lung capacity revisited Refer to Exercise 10.34 about measuring the lung function (called the forced vital capacity, or FVC, measured in liters) before and after using an inhaler. The data are shown again in the following table.Checkup 1 2 3 4 5 Before using inhaler: 5.08 5.99 5.32 6.03 5.44
10.57 Comparing book prices 2 For the data in the previous exercise, use software or a calculator to perform a significance test comparing the population mean prices.Show all steps of the test and indicate whether you would conclude that the mean price is lower at one of the two Internet bookstores.
10.56 Internet book prices Anna’s project for her introductory statistics course was to compare the selling prices of textbooks at two Internet bookstores. She first took a random sample of 10 textbooks used that term in courses at her college, based on the list of texts compiled by the college
10.49 Does exercise help blood pressure? Several recent studies have suggested that people who suffer from abnormally high blood pressure can benefit from regular exercise. A medical researcher decides to test her belief that walking briskly for at least half an hour a day has the 10.4 Practicing
10.46 Compare permutation test to t test Refer to the previous exercise.a. Run a t test and report the P-value for the two-sided alternative hypothesis.b. Using a significance level of 0.10, are the decisions based on the t test and based on the permutation test comparable? Which one would you
10.45 Time spent on social networks revisited Exercise 10.31 considered the following data on the number of hours students spent on social network sites per week:Males: 5, 7, 9, 10, 12, 12, 12, 13, 13, 15, 15, 20 Females: 5, 7, 7, 8, 10, 10, 11, 12, 12, 14, 14, 14, 16, 18, 20, 20, 20, 22, 23, 25,
10.44 Two-sided permutation P-value Refer to the previous exercise and the sampling distribution mentioned there.What is the permutation P-value for the two-sided test with alternative hypothesis that the mean improvement scores are different under therapies 1 and 2? (Hint: As for any regular test,
10.43 Permutations equally likely Refer to the previous exercise comparing improvement scores under two therapies for depression patients.a. State the null hypothesis of equal population distributions in the context of this experiment.b. Argue that if the null hypothesis is true, the sampling
10.42 Permuting therapies Refer to Exercise 10.38, which compared two therapies for depression patients. Suppose that in a different experiment, only four patients took part; two were randomly assigned to the group that received therapy 1 and the remaining two to the group that received therapy
10.41 Teeth whitening results One scientific “test of whiteness”tested the effect of a self applied tooth-whitening peroxide gel system in a randomized, controlled clinical trial.9 The 58 adults assigned to the gel whitening group applied the gel after normal brushing according to the
10.40 Vegetarians more liberal? When a sample of social science graduate students at the University of Florida gave their responses on political ideology (ranging from 1 = very liberal to 7 = very conservative ), the mean was 3.18 1s = 1.722 for the 51 nonvegetarian students and 2.22 1s = 0.672 for
10.39 Clinical therapies 2 Refer to the previous exercise.a. For the null hypothesis, H0: m1 = m2, show that t = 2.62 and the two-sided P@value = 0.059. Interpret.b. What decision would you make in the test, using a (i)0.05 and (ii) 0.10 significance level? Explain what this means in the context of
10.38 Comparing clinical therapies A clinical psychologist wants to choose between two therapies for treating severe cases of mental depression. She selects six patients who are similar in their depressive symptoms and in their overall quality of health. She randomly selects three of the patients
10.37 Surgery versus placebo for knee pain Refer to Example 10, “Arthroscopic Surgery.” Here we show MINITAB output comparing mean knee pain scores for the placebo (Group 1) to lavage arthroscopic surgery(Group 2) assuming equal population standard deviations.a. State and interpret the result
10.36 Body dissatisfaction test Refer to the previous exercise.a. Find the P-value for testing whether the population means are equal. Use a two-sided alternative.b. Summarize assumptions for the analysis in parta. Do you think the normality assumption is justified? If not, what is the consequence
10.35 Body dissatisfaction Female college student participation in athletics has increased dramatically over the past few decades. Sports medicine providers are aware of some unique health concerns of athletic women, including disordered eating. A study (M. Reinking and L. Alexander, Journal of
10.34 Vital capacity One of the authors of this book has his lung function checked every other year. At each checkup, his lung volume (called the forced vital capacity, or FVC)is measured before and after using an inhaler that contains medication against asthma. The last five checkups provided the
10.33 Normal assumption The methods of this section make the assumption of a normal population distribution. Why do you think this is more relevant for small samples than for large samples? (Hint: What shape does the sampling distribution of x1 - x2 have for large samples, regardless of the actual
10.32 More time on social networks In the previous exercise, plot the data. Do you see any outliers that could influence the results? Remove the most extreme observation from each group and redo the analyses. Compare results and summarize the influence of the extreme observations.
10.31 Time spent on social networks As part of a class exercise, an instructor at a major university asks her students how many hours per week they spend on social networks. She wants to investigate whether time spent on social networks differs for male and female students at this university. The
10.30 Gum flavor longevity In a test to determine the flavor longevity of a chewing gum, clients entering a store were asked to participate in an activity. The activity consisted of chewing a certain brand of gum and recording how long the gum flavor lasted in minutes. Records from groups of males
10.29 Study time A graduate teaching assistant for Introduction to Statistics (STA 2023) at the University of Florida collected data from students in one of her classes in spring 2007 to investigate whether study time per week(average number of hours) differed between students in the class who
10.28 Kidnapping in southern and eastern European countries The following data on kidnapping offences in countries of east and south Europe in 2014 were obtained from https://data.unodc.org.(Crime and Criminal Justice –> Crime –> Kidnapping –>Filter by Region and Sub Region as
10.27 Kuwaiti men versus Swedish men The following descriptive statistics were obtained from a study (Saud al-Obaidi et al., Journal of Rehabilitation Research and Development, vol. 40, 2003) that aimed to compare the weight of Kuwaiti men with Swedish men between the ages of 20 to 29 years.Group
10.26 Female and male monthly smokers Refer to the previous exercise. A subject was called a monthly smoker if he or she had smoked cigarettes over an extended period of time.The 74 female monthly smokers had a mean HONC score of 5.4 1s = 3.52, and the 71 male monthly smokers had a mean HONC score
10.25 Females or males more nicotine dependent? Refer to Exercise 10.23 about studying nicotine dependence using a random sample of teenagers. Of those seventh graders in the study who had tried tobacco, the mean HONC score was 2.8 1s = 3.62 for the 150 females and 1.6 1s = 2.92 for the 182
10.24 Inhaling affect HONC? Refer to the previous exercise.a. Show that the test statistic for H0: m1 = m2 equals t = 11.7. If the population means were equal, explain why it would be nearly impossible by random variation to observe this large a test statistic.b. What decision would you make about
10.23 Nicotine dependence A study on nicotine dependence for teenage smokers obtained a random sample of seventh graders. The response variable was constructed from a questionnaire called the Hooked on Nicotine Checklist(HONC). This is a list of ten questions such as, “Have you ever tried to quit
10.22 Empagliflozin and renal function over time A study published in June 2016 in New England Journal of Medicine wanted to determine the long-term renal effects (measured by eGFR: estimated glomerular filtration rate)of empagliflozin in patients with type 2 Diabetes. 7020 patients with type 2
10.21 Bulimia CI A study of bulimia among college women(J. Kern and T. Hastings, Journal of Clinical Psychology, vol. 51, 1995, p. 499) studied the connection between childhood sexual abuse and a measure of family cohesion(the higher the score, the greater the cohesion). The sample mean on the
10.17 More confident about housework Refer to part c in the previous exercise.a. Show that a 99% confidence interval is (10.0, 16.2).b. Explain why this interval is wider than the 95% confidence interval.
10.16 Housework for women and men Do women tend to spend more time on housework than men? If so, how much more? Based on data from the National Survey of Families and Households, one study reported the results in the table for the number of hours spent in housework per week. (Source: Data from A.
10.15 Address global warming You would like to determine what students at your school would be willing to do to help address global warming and the development of alternatively fueled vehicles. To do this, you take a random sample of 100 students. One question you ask them is, “How high of a tax
10.14 Energy drinks: health risks and toxicity A study was carried out in Saudi Arabia in which 31 male university students (18 overweight/obese and 13 having normal weight) were enrolled from December 2013 to December 2014 (www.annsaudimed.net). The heart rate variability was significantly less in
10.13 Prevalence of allergen-specific IgE antibodies in school children A study was conducted in Japan to estimate the prevalence of allergen-specific IgE antibodies in children. A group of school children between the ages of 9 and 15 years were surveyed in 2001 and in 1996 (retrospectively).The
10.11 Hormone therapy for menopause The Women’s Health Initiative conducted a randomized experiment to see whether hormone therapy was helpful for postmenopausal women. The women were randomly assigned to receive the estrogen plus progestin hormone therapy or a placebo.After five years, 107 of
10.10 Comparing marketing commercials Two TV commercials are developed for marketing a new product. A volunteer test sample of 200 people is randomly split into two groups of 100 each. In a controlled setting, Group A watches commercial A and Group B watches commercial B. In Group A, 25 say they
10.9 Basic life support knowledge and willingness to enroll in a first-aid course. In the study of basic life support knowledge mentioned in Exercise 10.3, 51.1% students from nonbiological subjects said they would enroll in a first-aid course versus 74.7% of students from biological subjects. Is
10.8 Significance test for aspirin and cancer deaths study In the study for cancer death rates, consider the null hypothesis that the population proportion of cancer deaths p1 for placebo is the same as the population proportion p2 for aspirin. The sample proportions were pn 1 = 347>11535 = 0.0301
10.7 Swedish study test Refer to the previous exercise.a. State the hypotheses that were tested.b. Explain how to interpret the P-value for the test.c. Even though the difference between the sample proportions was larger than in the Physicians Health Study(Examples 2–4), the P-value is larger
10.5 Risky behaviors among HIV positive female sex workers In 2014, questionnaire surveys were administrated among 181 female sex workers in the Yunnan province of China who confirmed themselves to be HIV positive (www.ncbi.nlm.gov/pubmed/26833008). The participants were divided into two age
10.4 Smoking and lung obstruction A National Center for Health Statistics data brief published in 2015 (Nr. 181)looked at the association between lung obstruction and smoking status in adults 40 to 79 years old. In a random sample of 6927 adults without any lung obstruction, 54.1% never smoked. In
10.3 Basic life support knowledge In 2015, a survey of firstyear university students in Brazil was conducted to determine if they knew how to activate the Mobile Emergency Attendance Service (MEAS). Of the 1038 respondents(59.5% studying biological sciences, 11.6% physical sciences, and 28.6%
10.2 Sampling sleep The 2011 Bedroom Sleep poll of a random sample of 1500 adults reported that respondents slept an average of 6.5 hours on weekdays and 7.2 hours on weekends, and that 21% of respondents got eight or more hours of sleep on weekdays, whereas 44% got eight or more hours of sleep on
10.1 Unemployment rate According to the Bureau of Labor Statistics, the official unemployment rate was 10.4%among blacks and 4.7% among whites as of February 2015. (www.bls.gov/).a. Identify the response variable and the explanatory variable.b. Identify the two groups that are the categories of the
10.5 Adjusting for the Effects of Other Variables
10.4 Analyzing Dependent Samples
10.3 Other Ways of Comparing Means, Including a Permutation Test
10.2 Quantitative Response:Comparing Two Means
10.53 Movies versus parties Refer to the previous two exercises.Using software, compare the responses on movies and parties using (a) all steps of a significance test and (b) a 95%confidence interval. Interpret results in context.
9.83 Hours at work When all subjects in the 2012 GSS who were working full- or part-time were asked how many hours they worked in the previous week at all jobs (variable HRS1), software produced the following analyses:For this printout,a. State the hypotheses.b. Explain how to interpret the values
9.82 Two ideal children? Is the ideal number of children equal or different from 2? For testing that the mean response from the 2014 GSS equals 2.0 for the question, “What do you think is the ideal number of children to have?” software shows results:a. Report the test statistic value and show
9.77 Interest charges on credit card A bank wants to evaluate which credit card would be more attractive to its customers, one with a high interest rate for unpaid balances but no annual cost or one with a low interest rate for unpaid balances but an annual cost of $40. For a random sample of 100
9.72 Protecting the environment? When the 2010 General Social Survey asked, “Would you be willing to pay much higher taxes in order to protect the environment?” (variable GRNTAXES), 459 people answered yes and 626 answered no. (We exclude those who made other responses.) Let p denote the
9.50 Decision errors in prostate cancer detection In the year 2016, approximately 181,000 new prostate cancer cases were expected to be diagnosed in the United States and approximately 26,100 deaths were linked to prostate cancer (www.uptodate.com/contents/screening-for-prostate-cancer). The
9.41 Sensitivity study Ideally, results of a statistical analysis should not depend greatly on a single observation. To check this, it’s a good idea to conduct a sensitivity study.This entails redoing the analysis after deleting an outlier from the data set or changing its value to a more typical
9.38 Selling a burger In Exercise 9.25, a fast-food chain compared two ways of promoting a turkey burger. In a separate experiment with 10 pairs of stores, the difference in the month’s increased sales between the store that used coupons and the store with the outside poster had a mean of $3000.
9.36 Water fluoridation Fluoridated water has fluoride at a level that is effective for preventing cavities. A study determined the number of cavity-free children (NCF)per 100 children in 16 North American cities BEFORE and AFTER public water fluoridation projects.Let m denote the population mean
9.31 Photovoltaic solar energy in Europe According to Eurostat, the yearly growth rate of renewable energy production from photovoltaic cells is, on average, 1.65 in Europe and 1.57 in Germany. However, the rate is likely to decrease with time.The StatCrunch output shows the results for a
9.24 Which cola? The 49 students in a class at the University of Florida made blinded evaluations of pairs of cola drinks. For the 49 comparisons of Coke and Pepsi, Coke was preferred 29 times. In the population that this sample represents, is this strong evidence that a majority prefers one of the
9.20 Gender bias in selecting managers For a large supermarket chain in Florida, a women’s group claimed that female employees were passed over for management training in favor of their male colleagues. The company denied this claim, saying it picked the employees from the eligible pool at random
9.16 Religion important in your life? Americans ages 18 to 29 are considered to be less religious than older Americans.According to recent studies by the Pew Forum on Religion& Public Life, fewer young adults are affiliated with a specific religion than older people today. And, compared with
8.128 Randomized response To encourage subjects to make honest responses on sensitive questions, the method of randomized response is often used. Let’s use your class to estimate the proportion who have had alcohol at a party. Before carrying out this method, the class should discuss what they
8.125 An alternative interval for the population proportion The large-sample confidence interval for a proportion substitutes pn for the unknown value of p in the formula for the standard deviation of pn. An alternative method to form a 95% confidence interval determines the endpoints of the
8.123 Opinions over time about the death penalty For many years, the General Social Survey has asked respondents whether they favor the death penalty for persons convicted of murder. Support has been quite high in the United States, one of few Western nations that currently has the death penalty.
8.104 Housework and gender Using data from the National Survey of Families and Households, a study (from S.South and G. Spitze, American Sociological Review, vol.59, 1994, pp. 327–347) reported the descriptive statistics in the following table for the hours spent on housework.Analyze these data.
8.93 Working mother In response to the statement on a recent General Social Survey, “A preschool child is likely to suffer if his or her mother works,” suppose the response categories (strongly agree, agree, disagree, strongly disagree) had counts (104, 370, 665, 169). Scores 12, 1, -1, -22
8.91 Females watching TV The GSS asked in 2008, “On the average day about how many hours do you personally watch television?” Software reports the results for females,a. Would you expect that TV watching has a normal distribution? Why or why not?b. On what assumptions is the confidence interval
8.88 Revisiting mountain bikes Use the Mountain Bike data file on the book’s website, shown also below.a. Form a 95% confidence interval for the population mean price of all mountain bikes. Interpret.b. What assumptions are made in forming the interval in part a? State at least one important
8.83 More time on emails per week Refer to the previous exercise. Interpret each item in the following printout for a sample of 7446 Americans.95% confidence interval results:m : Mean of variable Variable Sample Std. L. U. Mean Err. DF Limit Limit Hours spent 5.234 0.1106 7445 5.0174 5.451 on
8.78 Grandpas using e-mail When the GSS asked in 2012,“About how many hours per week do you spend sending and answering e-mail?” the nine males in the sample of age at least 80 responded:0, 0, 0, 1, 2, 3, 4, 4, 13a. The TI@83+>84 screen shot shows results of a statistical analysis for
8.68 Female belief in life after death Refer to the previous exercise. The following printout shows results for the females in the sample, where X = the number answering yes. Explain how to interpret each item, in context. Sample 1 x2 X N Sample p 822 977 0.841351 95% CI (0.818442, 0.864260)
8.40 Work hours per week The General Social Survey asked 40 respondents about the number of hours they usually work in a week. A researcher analyzing data from the 2014 GSS obtained the following StatCrunch output:95% confidence interval results:m : Mean of variablea. Show how to construct the
8.39 How often read a newspaper? For the FL Student Survey data file on the book’s website, software reports the results for responses on the number of times a week the subject reads a newspaper:a. Is it plausible that m = 7, where m is the population mean for all Florida students? Explain.b.
8.36 Time spent on e-mail When the GSS asked n = 1050 people in 2012, “About how many hours per week do you spend sending and answering e-mail?” (EMAILHR), the summary statistics were x = 6.89 and s = 13.05. TI output with these data (available on the book’s website)is shown in the screen
8.18 Stem cell research A Harris poll of a random sample of 2113 adults in the United States in October 2010 reported that 72% of those polled believe that stem cell research has merit. (Source: www.harrisinteractive.com/vault/Harris-Interactive-Poll-HealthDay-2010-10.pdf.) The results, presented
8.16 Favor death penalty In the 2012 General Social Survey, respondents were asked whether they favored or opposed the death penalty for people convicted of murder. Software shows results Sample X N 1 1183 1824 Sample p 0.648575 95% CI (0.626665, 0.670484) Here, X refers to the number of the
7.63 Simulate a sampling distribution The table (data are available on the book’s website) provides prices per night for all 51 available hotel rooms (as of December 2014) in Panama City Beach, Florida, for a week in March 2015(spring break). The distribution of these prices is characterized by m
7.62 Finite populations The formula s>1n for the standard deviation of x actually is an approximation that treats the population size as infinitely large relative to the sample size n. The exact formula for a finite population size N isa. When n = 300 students are selected from a college student
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