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a course in statistics with r
Mind On Statistics 5th Edition Jessica M Utts, Robert F Heckard - Solutions
5.70 In a planned survey about moviegoing, two questions that will be asked follow:• How many times per month do you go to the movies?• Do you consider yourself to be well-informed about recent movies or not?The questions could be asked in either order. Briefly explain how you think the
5.69 An example of an unnecessarily complex survey question is“Shouldn’t former drug dealers not be allowed to work in hospitals after they are released from prison?” Restate this question so that it is clearer.
5.68 A survey question will be asked to determine whether people think smoking should be banned at all airports.a. Write a version of the question that is as neutral and unbiased as possible.b. Write a version of the question that is likely to get people to respond that smoking should be forbidden
5.67 This is a modification of Exercise 1.35. Suppose listeners to a latenight radio talk show were asked to call and report whether or not they had ever seen a ghost.a. What is this type of sample called?b. Do you think the proportion reporting that they had seen a ghost for the radio poll would
5.66 This is also Exercise 1.12. A proposed study design is to leave 100 questionnaires by the checkout line in a student cafeteria.The questionnaire can be picked up by any student and returned to the cashier. Explain why this volunteer sample is a poor study design.
5.65 This is also Exercise 1.11. A popular Sunday newspaper magazine often includes a yesorno survey question such as “Do you think there is too much violence on television?”or “Do you think parents should use physical discipline?”Readers are asked to phone their answers to the magazine,
5.64 Find an example of a poll based on a selfselected sample.Report the wording of the questions and the number who chose each response. Comment on whether or not you think the results can be extended to any population.
5.63 Gastwirth (1988, p. 507) describes a court case in which Bristol Myers was ordered by the Federal Trade Commission to stop advertising that “twice as many dentists use Ipana as any other dentifrice” and that more dentists recommended it than any other dentifrice. Bristol Myers had based
5.62 Explain why the main problem with the Literary Digest poll is described as “volunteer response” and not “volunteer sample.”
5.61 Despite his success in 1936, George Gallup failed miserably in trying to predict the winner of the 1948 U.S. presidential election. His organization, as well as two others, predicted that Thomas Dewey would beat incumbent Harry Truman.All three used what is called quota sampling. The
5.60 In each part, indicate whether the sample should be called a selfselected sample or a convenience sample.a. A political scientist surveys the 80 people in a class he teaches to evaluate student political views.b. A soft drink company wants to know which of two of their drinks consumers prefer.
5.59 In each part, indicate whether the sample should be called a selfselected sample or a convenience sample.a. To assess passenger satisfaction, an airline distributed questionnaires to 100 passengers in the airline’s frequent flyer lounge. All 100 individuals responded, and 95 respondents said
5.58 A group of biologists wants to estimate the abundance of barrel cactus in a desert. They divide the desert into a grid of 100 rectangular areas but exclude 10 of those areas because they are difficult to access. The biologists then measure the density of cactus in a randomly selected sample of
5.57 A local government wants to determine whether taxpayers support increasing local taxes to provide more public funding to schools. They randomly select 500 schoolchildren from a list of all children enrolled in local schools and then survey the parents of these children about possible tax
5.56 Find an example of a survey routinely conducted by the U.S. government. (The Internet is a good source; for instance, try http://www.fedstats.gov.) Explain how the survey is conducted, and identify the type(s) of sampling used.
5.55 Is a sample that is found by using randomdigit dialing more like a stratified sample or a cluster sample? Explain.
5.54 Refer to Exercise 5.53. Give one advantage of each sampling method in the context of the problem.
5.53 Suppose a state has 10 universities, 25 fouryear colleges, and 50 community colleges, each of which offer multiple sections of an introductory statistics class each year.Researchers want to conduct a survey of students taking introductory statistics in the state. Explain a method for
5.52 In each part, identify whether the sample is a stratified random sample or a cluster sample.a. A class of 200 students is seated in 10 rows of 20 students per row. Three students are randomly selected from every row.b. An airline company randomly chooses one flight from a list of all
5.51 A class of 200 students is numbered from 1 to 200, and a table of random digits is used to choose 60 students from the class. Is the group of students selected a simple random sample, a stratified random sample, a cluster sample, or a systematic sample?
5.50 In a factory producing television sets, every 100th set produced is inspected. Is the collection of sets inspected a simple random sample, a stratified random sample, a cluster sample, or a systematic sample?
5.49 Refer to Exercise 5.48, which lists the right handspan measurements for 103 female college students.a. Draw three simple random samples of ten measurements each from this dataset (an individual can be in more than one of your samples). Explain how you chose the samples and list the ten
5.48 The right handspan measurements (in cm) for 103 female college students in Table 2.4 in Chapter 2 are given again here and in the pennstate1F dataset on the companion website.Females (103 Students): 20, 19, 20.5, 20.5, 20.25, 20, 18, 20.5, 22, 20, 21.5, 17, 16, 22, 22, 20, 20, 20, 20, 21.7,
5.47 A lottery game is played by choosing six whole numbers between 1 and 49. The grand prize is won if all six numbers chosen match the winning numbers drawn. We can think of choosing the winning numbers as the same thing as choosing a simple random sample of six numbers.a. What is the list of
5.46 There are 8000 items in a population, and these items are labeled by using fourdigit numbers ranging from 0000 to 7999. Use the following stream of random digits to select four items from the population. Explain how you determined your answer.76429 69730 23395 12694 43387
5.45 A radio station has a contest each day for a week in which the DJ randomly selects one birthday (month and day, not year) and announces it on the air. The first person with that birthday who calls the station wins a prize. A new birthday is selected for each of the 7 days, and the station
5.44 In Example 2.3 of Chapter 2 we learned that when students are asked to “randomly pick a number between 1 and 10”they are much more likely to choose 7 than any other number, and much less likely to choose 1 than any other number. Explain how you could actually “randomly pick a number
5.43 Define each of the following terms:a. Probability sampling plan.b. Simple random sample.
5.42 Samples can be chosen using a probability sampling plan and they can be chosen by selecting a simple random sample.One of these methods is a special case of the other.Explain which one is a special case of the other.
5.41 A college dean plans a student survey to estimate the percentage of currently enrolled students who plan to take classes during the next summer session. The desired margin of error for a 95% confidence interval is to be at most 5%.What is the necessary sample size?Section 5.3 Skillbuilder
5.40 An epidemiologist plans a survey to estimate the prevalence of Alzheimer’s disease in the population of adults aged 65 years or older. The desired margin of error for a 95% confidence interval is to be no more than 3%. What sample size is needed?
5.39 In which of the following three samples will the margin of error be the smallest? Explain. Assume that each sample is a random sample.Sample A: sample of n 5 1000 from a population of 10 million.Sample B: sample of n 5 2500 from a population of 200 million.Sample C: sample of n 5 400 from a
5.38 Explain whether the margin of error would increase, decrease, or remain the same as a result of each of the following changes:a. Increase the sample size from 1000 to 2000.b. Decrease the sample size from 1000 to 500.c. Increase the population size from 10 million to 20 million.
5.37 Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law that requires all automobile passengers to wear a seat belt.a. What would be the approximate margin of error if the researcher randomly sampled 400 adults?b. What sample
5.36 A soft drink company has a new recipe for one of its products, and it would like to know if a majority of consumers of its drinks prefer the new recipe over the old recipe. The company plans to ask a representative sample of the population to taste both drinks. The company will then measure
5.35 Refer to Exercise 5.33. One of the questions asked was, “Do you think there will or will not come a time when Israel and the Arab nations will be able to settle their differences and live in peace?” The choices and percentage choosing them were “Yes, will be a time” (49%), “No, will
5.34 The question about the importance of religion in Example 5.3 was asked in a survey of elementary statistics students at Penn State University from 2007 to 2010. The results were as follows:Very important: 730 5 21.4%Fairly important: 1512 5 44.3%Not very important: 1171 5 34.3%Total: 3417 5
5.33 An Internet report on a 1999 Gallup poll(http://www.gallup.com/poll/index.asp, August 2, 1999)included the following statement: “The results below are based on telephone interviews with a randomly selected national sample of 1021 adults, 18 years and older, conducted July 22–25, 1999. For
5.32 Suppose a national polling agency conducted 100 polls in a year, using proper random sampling, and reported a 95% confidence interval for each poll. About how many of those confidence intervals would we expect not to cover the true population value?
5.31 In the year leading up to a big election, there are many polls conducted to estimate what percent of the population is likely to vote for each candidate. The true percent can change during the year, so the polls are not necessarily estimating the same thing every time. Suppose 100 such polls
5.30 A CBS News poll conducted between December 17 and 22, 2009, asked a random sample of n 5 563 married adult Americans, “Would you say that your marriage with your spouse is better, worse or about the same as your parents’ marriage?” (http://www.pollingreport.com/life.htm, March 9, 2010).
5.29 In an ABC News poll conducted between January 21 and 26, 2000, a random sample of n 5 1006 adult Americans was asked, “Compared to buying things by mail order or in a store, do you think that buying things over the Internet poses more of a threat to your personal privacy, less of a threat,
5.28 Adapted from Exercises 1.9 and 1.10. What sample size produces each of the following as the approximate margin of error?a. Margin of error 5 .05 or 5%.b. Margin of error 5 .30 or 30%.General Section Exercises
5.27 This is also Exercise 1.8c. For a survey based on 2000 adults, what is the approximate margin of error?
5.26 In a CNN/Time poll conducted December 17–18, 1998, a sample of n 5 1031 adults in the United States was asked,“Do you think the police should or should not be allowed to collect DNA information from suspected criminals, similar to how they take fingerprints?” Of those sampled, 66%
5.25 In a random sample of 90 students at a university, 72 students(80% or .80 of the sample) say that they use a laptop computer.a. Calculate the conservative margin of error for the survey.b. Compute an approximate 95% confidence interval for the population proportion that uses a laptop computer.
5.24 A survey is planned to estimate the proportion of voters in a community who plan to vote for Candidate Y. Calculate the conservative margin of error, as a proportion and as a percentage, for each of the following possible sample sizes:a. n 5 100.b. n 5 400.c. n 5 900.
5.23 A television rating agency produces the ratings of television shows by asking a random sample of about 5000 households with TV sets what shows they watch. The rating for a show is the proportion (or percentage) of all televisions in the sample that were tuned in to the show. Calculate a
5.22 Give an example of a survey situation that is likely to produce each of the following types of bias:a. Response bias.b. Selection bias.Section 5.2 Skillbuilder Exercises
5.21 Give an example of a survey situation that is likely to produce nonparticipation bias.
5.20 The U.S. government gathers numerous statistics based on random samples, but every 10 years, it conducts a census of the U.S. population. What can it learn from a census that cannot be learned from a sample?
5.19 For each of the following situations, explain whether or not the Fundamental Rule for Using Data for Inference holds.a. Available Data: Salaries for a random sample of male and female professional basketball players.Research Question: Are women paid less than men who are in equivalent jobs?b.
5.18 For each of the following situations, explain whether or not the Fundamental Rule for Using Data for Inference holds.a. Available Data: Opinions on whether or not the legal drinking age should be lowered to 19 years old, collected from a random sample of 1000 adults in the state.Research
5.17 Refer to the three types of bias given in Section 5.1. Which type of bias do you think would be introduced in each of the following situations? Explain.a. A list of registered automobile owners is used to select a random sample for a survey about whether people think homeowners should pay a
5.16 Refer to the three types of bias given in Section 5.1. Which type of bias do you think would be introduced in each of the following situations? Explain.a. In a college town, college students are hired to conduct doortodoor interviews to determine whether city residents think there should be a
5.15 For each definition, identify the correct term for the type of bias being defined. Possible answers are selection bias, nonparticipation bias, and response bias.a. Participants respond differently from how they truly feel.b. The method for selecting the participants produces a sample that does
5.14 In each of the following situations, indicate whether the potential bias is a selection bias, a nonparticipation bias, or a response bias.a. A survey question asked of unmarried men was, “What is the most important feature you consider when deciding whether to date somebody?” The results
5.13 Refer to Exercise 5.12. Suppose that you randomly chose four of the CDs, and then randomly chose one song from each one. Would this be considered a simple random sample of the musician’s songs? Explain.General Section Exercises
5.12 A friend has recommended the work of a musician who has recorded five CDs, each containing ten selections. You decide to visit a music store and listen to a simple random sample of four songs. Explain how you could select the four songs.
5.11 Briefly explain the difference between a sample survey and a census.
5.10 In a class of 20 students (John, Maria, Inez, Bill, etc.), a simple random sample of two people will be selected from the class. Use the definition of a simple random sample to compare the chance that John and Maria will be the group selected with the chance that Maria and Bill will be the
5.9 Give an example of a situation in which a sample must be used because a census is not possible.
5.8 Briefly explain what it means to say that a survey method produces nonparticipation bias.
5.7 Briefly explain what it means to say that a survey method produces selection bias.
5.6 To estimate the percentage of households in the United States that use a DVD player, a researcher surveys a randomly selected sample of 500 households and asks about DVD player usage.a. What is the population of interest in this survey?b. What is the sample in this survey?
5.5 A political scientist surveys 400 voters randomly selected from the list of all registered voters in a community. The purpose is to estimate the proportion of registered voters who will vote in an upcoming election.a. What is the population of interest in this survey?b. What is the sample in
5.4 The median income for a random sample of households in a school district was found to be $56,300. From this information, the school board decided that the median income for all households in the district was probably between about$52,000 and $60,000. Describe the difference between descriptive
5.3 In each case, briefly discuss whether you think the available sample data can be used to make an inference about the larger population.a. The heights of women in a psychology class will be used to estimate the average height of all women at a college.b. Parents of children attending a daycare
5.2 For each of the following examples from the text, explain whether there would be more interest in descriptive statistics(for the acquired dataset only) or in inferential statistics(extending results to a larger population).a. Ages at death of first ladies.b. The relationship between nicotine
5.1 According to the Fundamental Rule for Using Data for Inference, when can available data be used to make inferences about a much larger group?
4.84 For this exercise use the Student2010 dataset on the companion website. 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 UseCell.b. Fill
4.83 For this exercise, use the Student0405 dataset on the companion website. The variable Seat gives student responses to where they prefer to sit in a classroom (Front, Middle, Back) and the variable ReligImp indicates how important students feel religion is in their lives (Very, Fairly,
4.82 For this exercise, use the GSS-08 dataset on the companion website. Write a paragraph that describes the relationship between race (respondent’s race) and cappun (opinion about capital punishment). Include a two-way table of counts and a relevant set of conditional percentages.
4.81 For this exercise, use the GSS-08 dataset on the companion website. The variable gunlaw has responses to a question about whether or not the respondent would favor a law requiring a police permit to be obtained before the purchase of any gun. The variable owngun indicates whether or not there
4.80 For this exercise, use the UCDavis2 dataset on the companion website. The variable Cheat contains answers to a question about whether or not the respondent would tell the instructor if he or she saw another student cheating on an examination.a. Create a two-way table for the relationship
4.79 For this exercise, use the UCDavis2 dataset on the companion website. The variable WtFeel contains UC Davis student responses to the question “Do you think you are:Underweight? About right? Overweight?”a. Create a contingency table for the relationship between Sex (female or male) and
4.78 According to a study on partner abuse reported by the Sacramento Bee (July 14, 2000, p. A6, Associated Press), 25% of women with male partners had been assaulted by their current or a former partner, whereas 11% of women with female partners had been assaulted. What is the relative risk of
4.77 In Exercise 4.37, data were given for admissions to two graduate programs for men and women. The data are given again here for use in this exercise, with the combined data presented as well.Program A Program B Combined Admit Deny Admit Deny Admit Deny Men 400 250 50 300 450 550 Women 50 25 125
4.76 “Saliva test predicts labor onset” was the headline of a Reuters Health story that appeared May 23, 2000, at the Yahoo! Health News website. The story described a medical test called SalEst. A positive SalEst test indicates an elevated estrogen level, and this knowledge may help to predict
4.75 Refer to Exercises 4.73 and 4.74. Find the odds ratio for remaining free of heart disease for men with no anger compared with men with the most anger. Give the result in a sentence that someone with no training in statistics would understand.
4.74 Refer to the data in Exercise 4.73, showing the frequency of coronary heart disease for men with no anger and men with the most anger. Show how the numbers in the following statement were calculated: The odds of remaining free of heart disease versus getting heart disease are about 24 to 1 for
4.73 Exercise 4.10 concerned the relationship between anger and the risk of coronary heart disease. Some computer output for a chi-square test is shown below. What do the results indicate about the relationship? Explain.Expected counts are printed below observed counts Heart Disease Yes No No Anger
4.72 Example 4.15 (p. 130) was about the relationship between hormone therapy and invasive breast cancer. One of the results reported in the paper was, “Absolute excess risks per 10,000 person-years attributable to estrogen plus progestin were . . . 8 more invasive breast cancers” (Writing
4.71 In Example 4.15 (p. 130), a statistically significant relationship was found between hormone therapy and invasive breast cancer. There were 166 cases of invasive breast cancer out of 8506 women taking hormones and 124 cases of invasive breast cancer out of 8102 women taking placebo.a. What is
4.70 Pagano and Gauvreau (1993, p. 133) reported data for women participating in the first National Health and Nutrition Examination Survey (Carter et al., 1989). The explanatory variable was whether or not the woman gave birth to her first child at the age of 25 or older, and the outcome variable
4.69 Compute the chi-square statistic, and assess the statistical significance for the relationship between smoking and time to pregnancy in Exercise 4.64. State a conclusion about the relationship.
4.68 Compute the chi-square statistic and assess the statistical significance for the relationship between bird ownership and lung cancer, based on the data in Exercise 4.65. State a conclusion about the relationship.
4.67 Refer to Example 4.2 (p. 116) and Exercise 4.66 about separation rates and smoking habits for Australian married couples. The following table of counts and row percentages compares couples in which one partner smoked to couples in which both partners smoked:Marital Status Smoking Separated Not
4.66 Example 4.2 (p. 116) described an Australian study in which married couples were surveyed in each of 3 consecutive years to learn what factors might be associated with marital separation. Table 4.3 (p. 116) gave data on smoking habits and whether the couple had separated during the study
4.65 In a study in Berlin, reported by Kohlmeier et al. (1992) and by Hand et al. (1994), researchers asked 239 lung-cancer patients and 429 controls (matched to the lung-cancer cases by age and sex) whether or not they had kept a pet bird during adulthood. Of the 239 lung-cancer cases, 98 said
4.64 Researchers asked women who were pregnant with planned pregnancies how long it took them to get pregnant (Baird and Wilcox, 1985; see also Weiden and Gladen, 1986).Length of time to pregnancy was measured ac cording to the number of cycles between stopping birth control and getting pregnant.
4.63 The following table contains data on ear piercings and tattoos for a sample of 1375 college women. The earpierce response is the total number of ear piercings for a woman, and this has been categorized in the rows of the table.Ear Piercings and Tattoos, 1375 College Women Piercings No Tattoo
4.62 Wechsler and Kuo (2000) used data from the 1999 College Alcohol Study to examine the relationship between student alcohol use and student definitions of binge drinking. In the study, approximately 14,000 college students from 119 schools answered questions about drinking habits. Using the
4.61 The following 2 3 2 contingency table shows data for sex and opinion about the legalization of marijuana for respondents in the 2008 General Social Survey in which a random sample of U.S. adults was surveyed. (Raw data are in the GSS-08 dataset on the companion website.)Opinion on Marijuana
4.60 In Example 4.15 (p. 130), a statistically significant relationship was found between hormone therapy and invasive breast cancer. In the same study, the following observed counts were found for death from coronary heart disease(CHD). Carry out the five steps leading to a conclusion about
4.59 Exercise 4.2 (p. 136) gave the following data from the General Social Survey for the relationship between whether individuals smoked and whether they had ever divorced, for respondents who had ever been married:Ever Divorced?Smoke? Yes No Total Yes 238 247 485 No 374 810 1,184 Total 612 1,057
4.58 In a 2012 survey of Internet users done by the Pew Center, respondents were asked whether they used social networking sites. The following 2 3 2 table of counts and row percentages displays the results by sex of the respondent:Use Social Networking Sites?Yes No Total Men 525 (62%) 321 (38%)
4.57 Considering the effect of sample size on the chi-square test, explain why a finding that a relationship is “not statistically significant” should not be interpreted as absolute proof that there is no relationship in the population.
4.56 Refer to Exercise 4.55.a. Suppose that 500 men and 500 women had been surveyed, rather than 50 of each sex as in Exercise 4.55.Further suppose that the proportions in favor of capital punishment remained the same, at 380/500 or 76% of the men and 320/500 or 64% of the women. Calculate the
4.55 Imagine that 50 men and 50 women are asked, “Do you favor or oppose capital punishment for those convicted of murder?” In the observed data, 38/50 5 .76, or 76% of the men favor capital punishment compared to 32/50 5 .64, or 64% of the women.a. Write null and alternative hypotheses about
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