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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions

9.22 Use of complementary and integrative health (CIH)strategies among nurses in Iran A study (J Integr Med.2016; 14(2): 121–127) was conducted between May 2014 and April 2015 to assess the knowledge, attitude, and use of CIH strategies among nurses in Iran. In this study, 157 nurses from two
9.21 Gender discrimination Refer to the 95% confidence interval shown in the MINITAB output in the previous exercise.What are the plausible values for the probability of a female to be selected for training? Is this in accordance with our decision of the significance test from part e of the
9.19 Testing a headache remedy Studies that compare treatments for chronic medical conditions such as headaches can use the same subjects for each treatment. This type of study is commonly referred to as a crossover design.With a crossover design, each person crosses over from using one treatment
9.18 Opinion on fracking a year earlier The question about the opinion on the increased use of fracking from the November 2014 survey mentioned in Example 6 was also included in an earlier survey in September 2013. Using this earlier survey, let’s again focus on those who oppose the increased use
9.17 Another test of astrology Examples 1, 3, and 5 referred to a study about astrology. Another part of the study used the following experiment: Professional astrologers prepared horoscopes for 83 adults. Each adult was shown three horoscopes, one of which was the one an astrologer prepared for
9.15 Dogs and cancer A recent study4 considered whether dogs could be trained to detect whether a person has lung cancer or breast cancer by smelling the subject’s breath.The researchers trained five ordinary household dogs to distinguish, by scent alone, exhaled breath samples of 55 lung and 31
9.14 Find test statistic and P-value For a test of H0: p = 0.50, the sample proportion is 0.35 based on a sample size of 100.a. Show that the test statistic is z = -3.0.b. Find the P-value for Ha: p 6 0.50.c. Does the P-value in part b give much evidence against H0? Explain.
9.13 Get more P-values from z Refer to the previous exercise.Suppose z = 2.50 instead of 1.04.a. Find the P-value for (i) Ha: p 7 0.50, (ii) Ha: p • 0.50, and (iii) Ha: p 6 0.50.b. Do any of the P-values in part a provide strong evidence against H0? Explain.
9.12 Get P-value from z For a test of H0: p = 0.50, the z test statistic equals 1.04.a. Find the P-value for Ha: p 7 0.50.b. Find the P-value for Ha: p • 0.50.c. Find the P-value for Ha: p 6 0.50. (Hint: The P-values for the two possible one-sided tests must sum to 1.)d. Do any of the P-values in
9.11 Believe in astrology? You plan to apply significance testing to your own experiment for testing astrology, in which astrologers have to guess which of four personality profiles is the correct one for someone who has a particular horoscope. Define the parameter of interest and state the
9.10 Customer satisfaction A customer of a car workshop claimed that majority of customers were not satisfied with the services provided. In order to test this claim, officials in charge of the workshop delegated a third-party statistical company to administrate a satisfaction survey of its current
9.9 P-value Indicate whether each of the following P-values gives strong evidence or not especially strong evidence against the null hypothesis.a. 0.38b. 0.001
9.8 z test statistic To test H0: p = 0.50 that a population proportion equals 0.50, the test statistic is a z-score that measures the number of standard errors between the sample proportion and the H0 value of 0.50. If z = 3.6, do the data support the null hypothesis, or do they give strong
9.7 Proper hypotheses? Suggest a way to correct each set of null and alternative hypotheses shown such that a proper set of hypotheses can be formed, and then illustrate them through an example.a. H0: pn = 0.50, Ha: pn 7 0.50b. H0: m = 10, Ha: m = 20c. H0: p 6 0.30, Ha: p = 0.10
9.6 Examples of hypotheses Give an example of a null hypothesis and an alternative hypothesis about a (a) population proportion and (b) population mean.
9.5 Low-carbohydrate diet A study plans to have a sample of obese adults follow a proposed low-carbohydrate diet for three months. The diet imposes limited eating of starches (such as bread and pasta) and sweets, but otherwise no limit on calorie intake. Consider the hypothesis, The population mean
9.4 Electricity prices According to the U.S. Energy Information Administration, the average monthly household electricity bill in 2014 was $114 before taxes and fees. A consumer association plans to investigate if the average amount has changed this year. Define the population parameter of interest
9.3 Burden of proof For a new pesticide, should the Environmental Protection Agency (EPA) bear the burden of proof to show that it is harmful to the environment, or should the producer of the pesticide have to show that it is not harmful to the environment? The pesticide is considered harmful if
9.2 H0 or Ha? State whether each of the following statements is a null hypothesis or an alternative hypothesis. Why?a. In 2016, the average price of solar energy in the United States was $3.70 per watt.b. At least 1 out of every 8 women in the United States will develop breast cancer during her
9.1 H0 or Ha? For parts a andb, is the statement a null hypothesis, or an alternative hypothesis?a. In Canada, the proportion of adults who favor legalized gambling equals 0.50.b. The proportion of all Canadian college students who are regular smokers is less than 0.24, the value it was 10 years
8.129 GSS project The instructor will assign the class a theme to study. Download recent results for variables relating to that theme from sda.berkeley.edu/GSS. Find and interpret confidence intervals for relevant parameters.Prepare a two-page report summarizing results.
8.127 Median as point estimate When the population distribution is normal, the population mean equals the population median. How good is the sample median as a point estimate of this common value? For a random sample, the standard error of the sample median equals 1.251s>1n2. If the population is
8.126 m and n Consider the sample size formula n = [pn 11 - pn 2z2]>m2 for estimating a proportion. When pn is close to 0.50, for 95% confidence explain why this formula gives roughly n = 1>m2.
8.124 Why called “degrees of freedom”? You know the sample mean x of n observations. Once you know 1n - 12 of the observations, show that you can find the remaining one. In other words, for a given value of x, the values of 1n - 12 observations determine the remaining one. In summarizing scores
8.122 Women’s satisfaction with appearance A special issue of Newsweek in March 1999 on women and their health reported results of a poll of 757 American women aged 18 or older. When asked, “How satisfied are you with your overall physical appearance?” 30% said very satisfied, 54% said
8.121 True or false Quadrupling the sample size n cuts the margin of error into half, other things being equal.
8.120 True or false If you have a volunteer sample instead of a random sample, then a confidence interval for a parameter is still completely reliable as long as the sample size is larger than about 30.
8.119 True or false The confidence interval for a mean with a random sample of size n = 2000 is invalid if the population distribution is bimodal.
8.118 True or false Suppose a 95% confidence interval for the population proportion of students at your school who regularly drink alcohol is (0.61, 0.67). The inference is that you can be 95% confident that the sample proportion falls between 0.61 and 0.67.
8.117 Interpret CI For the previous exercise, provide the proper interpretation.
8.116 Mean age at marriage A random sample of 50 records yields a 95% confidence interval of 21.5 to 23.0 years for the mean age at first marriage of women in a certain county. Explain what is wrong with each of the following interpretations of this interval.a. If random samples of 50 records were
8.115 Multiple choice: Why z? The reason we use a z-score from a normal distribution in constructing a large-sample confidence interval for a proportion is thata. For large random samples the sampling distribution of the sample proportion is approximately normal.b. The population distribution is
8.114 Multiple choice: Number of close friends Based on responses of 1467 subjects in a General Social Survey, a 95% confidence interval for the mean number of close friends equals (6.8, 8.0). Which two of the following interpretations are correct?a. We can be 95% confident that x is between 6.8
8.113 Multiple choice: CI property 2 Other things being equal, increasing n causes the margin of error of a confidence interval to (a) increase, (b) decrease, (c) stay the same.
8.112 Multiple choice: CI property Increasing the confidence level causes the margin of error of a confidence interval to (a) increase, (b) decrease, (c) stay the same.
8.111 What affects n? Using the sample size formula n = [pn 11 - pn 2z2]>m2 for a proportion, explain the effect on n of (a) increasing the confidence level and(b) decreasing the margin of error.
8.110 Outliers and CI For the observations 618, 650, 608, 634, 675, 618, 625, 619, 630 on Buy It Now prices for the iPhone 5s on eBay considered in Exercise 8.35, a confidence interval for the population mean Buy It Now price on eBay is (615, 647). Suppose the 5th observation was actually 875
8.109 Need 15 successes and 15 failures To use the large-sample confidence interval for p, you need at least 15 successes and 15 failures. Show that the smallest value of n for which the method can be used is (a) 30 when pn = 0.50, (b) 50 when pn = 0.30, (c) 150 when pn = 0.10. That is, the overall
8.108 99.9999% confidence Explain why confidence levels are usually large, such as 0.95 or 0.99, but not extremely large, such as 0.999999. (Hint: What impact does the extremely high confidence level have on the margin of error?)
8.107 Width of a confidence interval Why are confidence intervals wider when we use larger confidence levels but narrower when we use larger sample sizes, other things being equal?
8.106 Types of estimates An interval estimate for a mean is more informative than a point estimate, because with an interval estimate you can figure out the point estimate, but with the point estimate alone you have no idea how wide the interval estimate is. Explain why this statement is correct,
8.105 Women’s role opinions When subjects in a recent GSS were asked whether they agreed with the following statements, the (yes, no) counts under various conditions were as follows:j Women should take care of running their homes and leave running the country up to men: (275, 1556).j It is better
8.103 TV watching and race For the number of hours of TV watching, the 2008 GSS reported a mean of 2.98 for the 1324 white subjects, with a standard deviation of 2.66.The mean was 4.38 for the 188 black subjects, with a standard deviation of 3.58. Analyze these data, preparing a short report in
8.102 Religious beliefs A column by New York Times columnist Nicholas Kristof (August 15, 2003) discussed results of polls indicating that religious beliefs in the United States tend to be quite different from those in other Western nations. He quoted recent Gallup and Harris polls of random
8.101 Kicking accuracy A football coach decides to estimate the kicking accuracy of a player who wants to join the team. Of 10 extra-point attempts, the player makes all 10.a. Find an appropriate 95% confidence interval for the probability that the player makes any given extra point attempt.b.
8.100 Accept a credit card? A bank wants to estimate the proportion of people who would sign up for a credit card if it sends a particular mailing advertising it. For a trial mailing to a random sample of 100 potential customers, 0 people accept the offer. Can the bank conclude that fewer than 10%
8.99 Mean property tax A tax assessor wants to estimate the mean property tax bill for all homeowners in Madison, Wisconsin. A survey 10 years ago got a sample mean and standard deviation of $1400 and $1000.a. How many tax records should the tax assessor randomly sample for a 95% confidence
8.98 Adaptability to meet consumer demands In a survey conducted in 2016, Accenture (www.accenture.com)found that, in 2016, 40% of shoppers used smartphones more frequently to find what they wanted, as compared to 36% shoppers the year before. The 2016 survey has a 95% confidence level with a
8.97 Driving after drinking In December 2004, a report based on the National Survey on Drug Use and Health estimated that 20% of all Americans of ages 16 to 20 drove under the influence of drugs or alcohol in the previous year (AP, December 30, 2004). A public health unit in Wellington, New
8.96 Brexit In February 2016, a report was published in The Guardian. According to it, in a survey of 700 British and German firms by the Bertelsmann Foundation, 29%of them said they would either reduce capacities in the United Kingdom or relocate altogether in the event of a British exit or
8.95 Sex partners in previous year The 2008 General Social Survey asked respondents how many sex partners they had in the previous 12 months (variable PARTNERS).Software summarizes the results of the responses by Variable N Mean StDev SE Mean 95% CI partners 1766 1.1100 1.2200 0.0290 (1.0531,
8.94 Miami spring break For a trip to Miami, Florida, over spring break 2014, the following data (obtained from travelocity.com) are a random sample of hotel prices per night (in $) for a double room:239 237 245 310 218 175 330 196 178 245 255 190 330 124 162 190 386 145.a. Construct a histogram
8.92 Males watching TV Refer to the previous exercise. The 626 males had a mean of 2.87 and a standard deviation of 2.61. The 95% confidence interval for the population mean is (2.67, 3.08). Interpret in context.
8.90 Income for families in public housing A survey is taken to estimate the mean annual family income for families living in public housing in Chicago. For a random sample of 29 families, the annual incomes (in hundreds of dollars)are as follows:90 77 100 83 64 78 92 73 122 96 60 85 86 108 70 139
8.89 eBay selling prices For eBay auctions of the Samsung S5 16GB smartphone (unlocked and in new condition), a sample was taken in July 2014 where the Buy It Now prices were (in dollars):549, 600, 560, 519, 535, 570, 600, 625, 640, 550, 575, 600a. Explain what a parameter might represent that you
8.87 Happy often? The 1996 GSS asked, “How many days in the past seven days have you felt happy?” (This was the most recent year this question was posed.)a. Using the GSS variable HAPFEEL, verify that the sample had a mean of 5.27 and a standard deviation of 2.05. What was the sample size?b.
8.86 How often feel sad? Refer to the previous exercise.This question was asked of 10 students in a class at the University of Wisconsin recently. The responses were 0, 0, 1, 0, 7, 2, 1, 0, 0, 3.Find and interpret a 90% confidence interval for the population mean and indicate what you would have to
8.85 How often do women feel sad? A recent GSS asked,“How many days in the past seven days have you felt sad?” The 816 women who responded had a median of 1, mean of 1.81, and standard deviation of 1.98. The 633 men who responded had a median of 1, mean of 1.42, and standard deviation of
8.84 How long lived in town? The General Social Survey has asked subjects, “How long have you lived in the city, town, or community where you live now?” The responses of 1415 subjects in one survey had a mode of less than 1 year, a median of 16 years, a mean of 20.3, and a standard deviation of
8.82 Time spent on emails per week In a survey conducted in 2014, the General Social Survey (GSS) asked a sample of 7446 Americans how many minutes or hours they spent sending and answering emails. The results showed an average of 5.234 hours of email usage per week with a standard deviation of
8.81 Fuel efficiency The government website fueleconomy.gov has data on thousands of cars regarding their fuel efficiency. A random sample from this website of SUVs manufactured between 2012 and 2015 gives the following data on the combined (city and highway) miles per gallon (mpg):26, 23, 21, 23,
8.80 t-scoresa. Show how the t-score for a 95% confidence interval changes as the sample size increases from 10 to 20 to 30 to infinity.b. What does the answer in part a suggest about how the t distribution compares to the standard normal distribution?
8.79 Travel to work As part of the 2000 census, the Bureau of the Census surveyed 700,000 households to study transportation to work. It reported that 76.3% drove alone to work, 11.2% carpooled, 5.1% took mass transit, 3.2% worked at home, 0.4% bicycled, and 3.8% took other means.a. With such a
8.77 More NSA spying Refer to the previous exercise.a. Of the 1001 adults surveyed in Turkey, 49% said yes to the question from the Pew Research Center, resulting in a 95% confidence interval of (0.46, 0.52).True or false: We can be 95% confident that less than half of Turkey’s population thinks
8.76 Edward Snowden A report from the Pew Research Center found that disclosures by former National Security Administration (NSA) contractor Edward Snowden about NSA spying have damaged one major element of America’s global image: its reputation for protecting individual liberties. One question
8.75 Streaming A Harris Poll of 2300 U.S. adults surveyed online in April 2014 reports that 43% regularly watch television shows through streaming. (Source: “Cable Is King but Streaming Stands Strong When It Comes to Americans’TV Viewing Habits,” available at harrisinteractive.com)a. Find a
8.74 Insomnia in France A team of scientific researchers conducted a study on insomnia in France (Journal of Sleep Research, 9(1):35–42, April 2000). They used a representative sample of the French population that included 12,778 individuals. Among them, 73% complained of a nocturnal sleep
8.73 Legalize marijuana? The General Social Survey has asked respondents, “Do you think the use of marijuana should be made legal or not?” Go to the GSS website, sda.berkeley.edu/GSS. For the 2008 survey with variable GRASS:a. Of the respondents, how many said “legal” and how many said
8.72 Wife supporting husband Consider the statement that it is better for the man to work and the woman to tend the home, from the GSS (variable denoted FEFAM).a. Go to the sda.berkeley.edu/GSS website. Find the number who agreed or strongly agreed with that statement and the sample size for the
8.71 Population data You would like to find the proportion of bills passed by Congress that were vetoed by the president in the last congressional session. After checking congressional records, you see that for the population of all 40 bills passed, 15 were vetoed. Does it make sense to construct a
8.70 Alternative therapies The Department of Public Health at the University of Western Australia conducted a survey in which they randomly sampled general practitioners(GP) in Australia. One question asked whether the GP had ever studied alternative therapy, such as acupuncture, hypnosis,
8.69 Work agreement for nannies According to a 2016 poll of families in New York City who employ a nanny, 75%did not enter into a written work agreement with them.a. What has to be assumed about this sample to construct a confidence interval for the population proportion of all families who did not
8.67 Life after death The variable POSTLIFE in the 2012 General Social Survey asked, “Do you believe in life after death?” A report based on these data stated that “81% of Americans believe in life after death. The margin of error for this result is plus or minus 1.8%.” Explain how you
8.66 Technology and productivity In 2014, a survey was conducted among a sample of adults who use the Internet. It included 535 respondents employed in full-time or parttime jobs. 46% of online workers felt their productivity increased because of using the Internet, email, and cell phones (Source:
8.65 British monarchy After the British monarchy celebrated its diamond jubilee in 2012, a July poll conducted by YouGov.com and the Sunday Times of 1,667 British residents showed that 86% think the Queen personally has done a good job during her time on the throne, and 73% think that Britain
8.64 Approval rating for president In July 2014, midway through his second term as president, Gallup estimated Obama’s approval rate at 42%. According to gallup.com, “. . . [R]esults are based on telephone interviews with approximately 1,500 national adults; margin of error is {3 percentage
8.63 Unemployed college grads The U.S Bureau of the Census reports that based on data from the American Community Survey in 2012, 3.6 percent of all college graduates between the ages of 25 and 64 were unemployed. A larger percentage of men than women were unemployed:3.7 percent and 3.5 percent,
8.62 Bootstrap interval for the proportion We want a 90%confidence interval for the population proportion of students in a high school in Dallas, Texas, who can correctly find Iraq on an unlabeled globe. For a random sample of size 50, 5 get the correct answer.a. Access the Sampling Distribution of
8.61 Bootstrap interval for the mean In 2014, the General Social Survey interviewed 1399 randomly selected U.S.residents about how much time per week they spent surfing the web. The responses revealed a very right-skewed distribution, with a sample mean of 12 hours and a standard deviation of 15
8.60 Bootstrap technique for estimation A quality control process consists of crashing cars at various speeds. For a sample of 10 crash tests, the closing speed values (in kilometers per hour) were 61.83, 61.8, 31.82, 61.63, 32.32 32.52, 56.14, 61.67, 56.36, 56.57a. Explain the steps of how the
8.59 Why bootstrap? Explain the purpose of using the bootstrap method.
8.58 Google Glass Google started selling Google Glass (a type of wearable technology that projects information onto the eye) in the United States in spring 2014 for $1500. A national poll reveals that out of 500 people sampled, nobody owned Google Glass.a. Find the sample proportion who don’t own
8.57 Movie recommendation In a quick poll at the exit of a movie theater, 8 out of 12 randomly polled viewers said they would recommend the movie to their friends.a. Construct an appropriate 95% confidence interval for the population proportion.b. Is it plausible that only half of all the viewers
8.56 Do students like statistics? All respondents out of a random sample of ten students in a college said that they like statistics. Now you want to estimate the proportion of students who like statistics in the whole college.a. Find the sample proportion of students who like statistics.b. Find
8.55 Web survey to get large n A newspaper wants to gauge public opinion about legalization of marijuana. The sample size formula indicates that it need a random sample of 875 people to get the desired margin of error. But surveys cost money, and it can only afford to randomly sample 100 people.
8.54 Population variability Explain the reasoning behind the following statement: “In studies about a very diverse population, large samples are often necessary, whereas for more homogeneous populations smaller samples are often adequate.” Illustrate for the problem of estimating mean income
8.53 Income of Native Americans How large a sample size do we need to estimate the mean annual income of Native Americans in Onondaga County, New York, correct to within $1000 with probability 0.99? No information is available to us about the standard deviation of their annual income. We guess that
8.52 Farm size An estimate is needed of the mean acreage of farms in Ontario, Canada. A 95% confidence interval should have a margin of error of 25 acres. A study 10 years ago in this province had a sample standard deviation of 200 acres for farm size.a. About how large a sample of farms is
8.51 Employment percentage in the United States According to the U.S. Bureau of Labor Statistics, 80.3% out of the nation’s 81.4 million families had at least one employed member in 2015 (Source: http://www.bls.gov/news.release/famee.nr0.htm). What should be the sample size needed to estimate the
8.50 How many businesses fail? A study is planned to estimate the proportion of businesses started in the year 2006 that had failed within five years of their start-up. How large a sample size is needed to guarantee estimating this proportion correct to withina. 0.10 with probability 0.95?b. 0.05
8.49 Abstainers The Harvard study mentioned in the previous exercise estimated that 19% of college students abstain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it to within 0.05 with probability 0.95, if before conducting
8.48 Binge drinkers A study at the Harvard School of Public Health found that 44% of 10,000 sampled college students were binge drinkers. A student at the University of Minnesota plans to estimate the proportion of college students at that school who are binge drinkers. How large a random sample
8.47 Unemployment percentage A statistician conducts a study in order to estimate the proportion of families living in a poor area of a city and having at least one unemployed member. Calculate the sample size needed to estimate it to within 0.05 with 95% confidence.
8.46 Simulating the confidence interval Go to the Inference for a Mean web app, accessible on the book’s website. Select the Explore Coverage tab and keep the default skewed shape for the population distribution as well as the default confidence level of 95%. Set the sample size to 30 and
8.45 Number of children For the question, “How many children have you ever had?” use the GSS website sda.berkeley.edu/GSS with the variable CHILDS to find the sample mean and standard deviation for the 2012 survey. (Use YEAR(2012) as filter and select Summary Statistics under Options.) (Treat
8.44 Catalog mail-order sales A company that sells its products through mail-order catalogs wants information about the success of its most recent catalog. The company decides to estimate the mean dollar amount of items ordered from those who received the catalog. For a random sample of 100
8.43 Effect of confidence level Find the margin of error for estimating the population mean when the sample standard deviation equals 100 for a sample size of 25, using confidence levels (i) 95% and (ii) 99%. What is the effect of the choice of confidence level? (You can use Table B in the back to
8.42 Effect of n Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 100, with a sample size of (i) 25 and (ii) 100. What is the effect of increasing the sample size? (You can use Table B in the back to find the
8.41 Length of hospital stay for childbirth Data was collected from the records of 2962 patients admitted to a hospital in 2015 to estimate the mean length of stay for childbirth.It was observed that the sample mean was 2.372 days and the margin of error for estimating the population mean is 0.029
8.38 Wage discrimination? According to a union agreement, the mean income for all senior-level assembly-line workers in a large company equals $500 per week. A representative of a women’s group decides to analyze whether the mean income for female employees matches this norm.For a random sample

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