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essential statistics

Essential Statistics 1st Edition David S Moore - Solutions

14.33 A test goes wrong. Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:6.47 7.51 10.10 13.63 9.91 These data match the conditions for a ?: test better than real data
14.32 Predicting success of trainees. What distinguishes managerial trainees who eventually become executives from those who don't succeed and leave the company? We have lots of data on past trainees—data on their personalities and goals, their college preparation and performance, even their
14.31 Why are larger samples better? Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample (or the number of subjects in an experiment) on each of the following:(a) The margin of error of a 95% confidence interval.(b) The P -value of a test, when Ho is
14.30 What is significance good for? Which of the follow ing questions does a test of significance answer? Briefly explain your replies.(a) Is the sample or experiment properly designed?(b) Is the observed effect due to chance?(c) Is the observed effect important?
14.29 When to use pacemakers. A medical panel prepared guidelines for when cardiac pacemakers should be implanted in patients with heart problems. The panel reviewed a large num ber of medical studies to judge the strength of the evidence supporting each recommendation. For each recommendation,
14.28 Can we trust this interval? Here are data on the percent change in the total mass (in tons) of wildlife in several West African game preserves in the years 1971 to 1999:'1971 1972 1973 1974 1975 1976 1977 1978 2.9 3.1 -1.2 -1.1 -3.3 3.7 1.9 -0.3 1979 1980 1981 1982 1983 1984 1985 1986 -5.9
14.27 An outlier strikes. You have data on an SRS of recent graduates from your college that shows how long each student took to complete a bachelor's degree. The data contain one high outlier. Will this outlier have a greater effect on a confi dence interval for mean completion time if your sample
14.26 College degrees. At the Census Bureau Web site www.census.gov you can find the percent of adults in each state who have at least a bachelor's degree. It makes no sense to find x for these data and use it to get a confi dence interval for the mean percent /U. in all 50 states. Why not?
14.25 Pulling wood apart. You want to estimate the mean load needed to pull apart the pieces of wood in Exercise 13.43(page 254) to within ±1000 pounds with 95% confidence. How large a sample is needed?
14.24 Sensitive questions. The National AIDS Behavioral Surveys found that 170 individuals in its random sample of 2673 adult heterosexuals said they had multiple sexual part ners in the past year. That's 6.36% of the sample. Why is this estimate likely to be biased? Does the margin of error of a
14.23 Hotel managers. In Exercise 13.35 (page 253) you car ried out a test of significance based on the femininity scores of 148 male general managers of three-star and four-star ho tels. You now realize that a confidence interval for the mean score of male hotel managers would he more informative
14.22 Sampling at the mall. A market researcher chooses at random from women entering a large suburban shopping mall.One outcome of the study is a 95% confidence interval for the mean of "the highest price you would pay for a pair of casual shoes."(a) Explain why this confidence interval does not
14.21 Hotel managers. In Exercise 13.35 (page 253) you car ried out a test of significance based on data from 148 general managers of three-star and four-star hotels. Before you trust your results, you would like more information about the data.What facts would you most like to know?
14.20 Color blindness in Africa. An anthropologist claims that color blindness is less common in societies that live by hunting and gathering than in agricultural societies. He tests a number of adults in two populations in Africa, one of each type. The proportion of color-blind people is
14.19 A laboratory scale is known to have a standard devi ation of a = 0.001 gram in repeated weighings. Scale read ings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. How many times must you weigh a specimen on this scale in otder to get a
14.18 Vigorous exercise helps people live several years longer(on the average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in
14.17 A writer in a medical journal says: "An uncontrolled experiment in 17 women found a significantly improved mean clinical symptom score after treatment. Methodologic flaws make it difficult to interpret the results of this study." The writer is skeptical about the significant improvement
14.16 Many sample surveys use well-designed random samples but half or more of the original sample can't be contacted or refuse to take part. Any errors due to this nonresponse(a) have no effect on the accuracy of confidence intervals.(b) are included in the announced margin of error.(c) are in
14.15 You turn your Web browser to the online Harris Inter active poll. Based on 6748 responses from people who chose to click on this site, the poll reports that 16% of U.S. adults some times use the Internet to make telephone calls.'' You should refuse to calculate a 95% confidence interval based
14.14 The coach of a college men's basketball team records the resting heart rates of the 15 team members. You should not trust a confidence interval for the mean resting heart rate of all male students at this college based on these data because(a) with only 15 observations, the margin of error
14.13 The most important condition for sound conclusions from statistical inference is usually(a) that the data can be thought of as a random sample from the population of interest.(b) that the population distribution is exactly Normal.(c) that the data contain no outliers.
14.12 Searching for ESP. A researcher looking for evidence of extrasensory perception(ESP) tests 500 subjects. Four of these subjects do significantly better (P < 0.01) than random guessing.(a) You can't conclude that these four people have ESP. Why not?(b) What should the researcher now do to test
14.11 Confidence intervals help. Give a 95% confidence interval for the mean pH jj, for each sample size in the previous exercise. The intervals, unlike the P-values, give a clear picture of what mean pH values are plausible for each sample.
14.10 Detecting acid rain. Emissions of sulfur dioxide by industry result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall
14.9 Is it significant? In the absence of special preparation SAT mathematics scores in recent years have varied Normally with mean /t, = 518 and cr = 114. Fifty students go through a rigorous training program designed to raise their scores. Either by hand or by using software, carry out a test of
14.8 Number skills of young men. Suppose that scores of men aged 21 to 25 years on the quantitative part of the National Assessment of Educational Progress (NAEP) test follow a Normal distribution with standard deviation a = 60. You want to estimate the mean score within ±10 with 90% confidence.
14.7 Body mass index of young women. Example 13.1 (page 232) assumed that the body mass index (BMI) of all American young women follows a Normal distribution with standard deviation cr = 7.5. How large a sample would be needed to estimate the mean BMI /.t in this population to within ±1 with 95%
14.6 Is your food safe? "Do you feel confident or not confident that the food available at most grocery stores is safe to eat?" When a Gallup Poll asked this question, 87% of the sample said they were confident.^ Gallup announced the poll's margin of error for 95%confidence as ±3 percentage
14.5 Sample size and margin of error. Example 13.1 (page 232) described NHANES sur vey data on the body mass index (BMl) of 654 young women. The mean BMl in the sample was x = 26.8. We treated these data as an SRS from a Normally distributed pop ulation with standard deviation cr = 7.5.(a) Suppose
14.4 Confidence level and margin of error. Example 13.1 (page 232) described NHANES survey data on the body mass index (BMl) of 654 young women. The mean BMl in the sample was x = 26.8. We treated these data as an SRS from a Normally distributed population with standard deviation a = 7.5.(a) Give
14.3 Sampling shoppers. A marketing consultant observes 50 consecutive shoppers at a supermarket on a Sunday morning, recording how much each shopper spends in the store. Suggest some reasons why it may be risky to act as if these shoppers are an SRS of all shoppers at this store.
14.2 Running red lights. A survey asked a sample of licensed drivers, "Of every ten motorists who run a red light, about how many do you think will be caught?" The mean result for 880 respondents was x = 1.92 and the standard deviation was s = 1.83.^ For this large sample, s will be close to the
14.1 Rate that movie. A professor interested in the opinions of college-age adults about a new hit movie asks the 25 students in her course on documentary filmmaking to rate the entertainment value of the movie on a scale of 0 to 5. Which of the following is the most important reason why a
13.51 Tests from confidence intervals. A 95% confidence interval for a population mean is 31.5 ± 3.4. Use the method described in the previous exercise to answer these questions.(a) With a two-sided alternative, can you reject the null hy pothesis that fx = 34 at the 5% (a = 0.05) significance
13.50 Tests from confidence intervals. A confidence in terval for the population mean fx tells us which values of jx are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test
13.49 This wine stinks. Are untrained students less lili sensitive on the average than trained tasters in detect ing "off-odors" in wine? Exercise 13.47 gives the lowest lev els of dimethyl sulfide (DMS) that 10 students could detect.The units are micrograms of DMS per liter of wine (/xg/1). As
13.48 Eye grease. Athletes performing in bright sun-Ki light often smear black eye grease under their eyes to re duce glare. Does eye grease work? In one study, 16 student sub jects took a test of sensitivity to contrast after 3 hours ftrcing into bright sun, both with and without eye grease. This
13.47 This wine stinks. Sulfur compounds cause "off-Hiix odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of
13.46 Bone loss by nursing mothers. Exercise 13.44■in gives the percent change in the mineral content of the spine for 47 mothers during three months of nursing a baby. As in that exercise, suppose that the percent change in the popula tion of all nursing mothers has a Normal distribution with
13.45 Pulling wood apart. Exercise 13.43 gives data on Hii the pounds of load needed to pull apart pieces of Douglas fir. The data are a random sample from a Normal distribution with standard deviation 3000 pounds.(a) Is there significant evidence at the a = 0.10 level against the hypothesis that
13.44 Bone loss by nursing mothers. Breast-feeding tL mothers secrete calcium into their milk. Some of the cal cium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in mineral content of the spines of 47 mothers during three months of
13.43 Pulling wood apart. How heavy a load (pounds)Mil is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a lab oratory exercise:33,190 31,860 32,590 32,320 33,020 32,030 23,040 30,930 32,720 24,050 30,170 31,300 26,520 33,280 30,460
13.42 The wrong P. The report of a study of seat belt use by drivers says, "Hispanic drivers were not significantly more likely than White/non-Hispanic drivers to overreport safety belt use(27.4 vs. 21.1%, respectively; z = 1.33, P > 1.0)."'^ How do you know that the P -value given is incorrect?
13.41 The wrong alternative. One of your friends is com paring movie ratings by female and male students for a class project. She starts with no expectations as to which sex will rate a movie more highly. After seeing that women rate a particular movie more highly than men, she tests a one-sided
13.40 5% versus 1 %. Sketch the standard Normal curve for the z test statistic and mark off areas under the curve to show why a value of z that is significant at the 1% level in a one sided test is always significant at the 5% level. If ^ is significant at the 5% level, what can you say about its
13.39 Forests and windstorms. Does the destruction of large trees in a windstorm change forests in any important way?Here is the conclusion of a study that found that the answer is"No":
13.38 Cicadas as fertilizer? Every 17 years, swarms of ci cadas emerge from the ground in eastern North America, live for about six weeks, then die. There are so many cicadas that their dead bodies can serve as fertilizer. In an experiment, a re searcher added cicadas under some plants in a natural
13.37 Pig skulls show that you were rich. In grave sites from ancient China, skulls of sacrificed pigs tend to appear along with expensive ornaments. This suggests that the pigs, like the ornaments, signal the wealth and prestige of the per son buried. A study of burials from around 3500 B.C.
13.36 Is this what P means? When asked to explain the meaning of "the P-value was P = 0.03," a student says, "This means there is only probability 0.03 that the null hypothesis is true." Explain what P = 0.03 really means in a way that makes it clear that the student's explanation is wrong.
13.35 Hotel managers' personalities. Successful hotel managers must have personality characteristics often thought of as feminine (such as "compassionate") as well as those of ten thought of as masculine (such as "forceful"). A personality test measures "femininity" on a scale of 1 to 7. A sample
13.34 I want more muscle. If young men thought that their own level of muscle was about what women prefer, the mean"muscle gap" in the study described in Exercise 13.30 would be 0. We suspect (before seeing the data) that young men think women prefer more muscle.(a) State null and alternative
13.33 Student study times. Exercise 13.29 describes a class survey in which students claimed to study an average of x =137 minutes on a typical weeknight. Regard these students as an SRS from the population of all first-year students at this uni versity. Does the study give good evidence that
13.32 Explaining confidence. Here is an explanation from the Associated Press concerning one of its opinion polls. Ex plain briefly but clearly in what way this explanation is incor rect.For a poll of 1,600 adults, the variation due to sampling error is no more than three percentage points either
13.31 An outlier strikes. There were actually 270 responses to the class survey in Exercise 13.29. One student claimed to study 30,000 minutes per night. We know he's joking, so we left out this value. If we did a calculation without looking at the data, we would get x = 248 minutes for all 270
13.30 I want more muscle. Young men in North America and Europe tend to think they need more muscle to be attrac tive. One study presented 200 young American men with 100 images of men with various levels of muscle.^ Researchers mea sure level of muscle in kilograms per square meter (kg/m^) of
13.29 Student study times. A class survey in a large firstyear college class asked, "About how rnany minutes do you study on a typical weeknight?" The mean response of the 269 studeiats was x = 137 minutes. Suppose that we know that study time follows a Normal distribution with standard devia tion
13.28 Stating hypotheses. In planning a study of the birth weights of babies whose mothers did not see a doctor before delivery, a researcher states the hypotheses as Hq: X — 1000 grams Ha'-X < 1000 grams What's wtong with this?In all exercises that call for P-values, give the actual value if you
13.27 Women's heights. The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year's female graduates from your local high school is different from the national avetage. You measure an SRS of 78 female graduates and find that x = 63.1 inches.What
13.26 You use software to carry out a test of significance. The program tells you that the P-value is P = 0.027. This means that(a) the probability that the null hypothesis is true is 0.027.(b) the value of the test statistic is 0.027.(c) a test statistic as extreme as these data give would happen
13.25 You use software to carry out a test of significance. The program tells you that the P-value is P = 0.027. This result is(a) not significant at either a = 0.05 ora = 0.01.(b) significant at a = 0.05 but not at a = 0.01.(c) significant at both a = 0.05 and a = 0.01.
13.24 The alternative hypothesis for the test in Exercise 13.23 is(a) Ha'. i-L 18. (b) Hfl: II < 18. (c) H,: pt = 16.5.
13.23 Psychologists often measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as
13.22 Another specimen is weighed 8 times on this scale. The average weight is 4.1602 grams. A 99% confidence interval for the ttue weight of this specimen is(a) 4.1602 ± 0.00032. (b) 4.1602 ± 0.00069.(c) 4.1602 ±0.00091.
13.21 The Z statistic for testing Hq: ii = 3.41 based on these 3 measurements is(a) z = 0.004. (b) z = 4. {c) z = 6.928.
13.20 A 95% confidence interval for the ttue weight of this specimen is(a) 3.414 ±0.00113. (b) 3.414 ± 0.00065.(c) 3.414 ±0.00196.
13.19 Testing software. You have computer .software that is supposed to generate observa tions from a standard Normal distribution. If this is true, the numbers generated come from a population with pi — 0 and a = I. A command to generate 100 observations gives outcomes with mean x = —0.2213.
13.18 Significance from a table. A test of Hq: m = 1 against pt ^ 1 has test statistic Z = 1.776. Is this test significant at the 5% level (a = 0.05)? Is it significant at the 1%level?
13.17 Significance from a table. A test of Hq: m = 1 against H,: /x > 1 has test statistic t; = 1.776. Is this test significant at the 5% level (a = 0.05)? Is it significant at the 1%level (a — 0.01)?
13.16 Protecting long-distance runners. A randomized comparative experiment com pared vitamin C with a placebo as protection against respiratory infections after run ning a very long distance. The report of the study said:^(a) Explain to someone who knows no statistics why "significantly more"
13.15 Reading a computer screen. Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in an average time of 22 seconds in the common Times New Roman font. Ask 25 adults to read this text in the ornate font named Gigi. Here are
13.14 Measuring conductivity. Here are 6 measurements of the electrical conductivity of a liquid:5.32 4.88 5.10 4.73 5.15 4.75 The liquid is supposed to have conductivity 5. Do the measurements give good evidence that the true conductivity is not 5 ?The 6 measurements are an SRS from the population
13.13 The Z statistic. Published reports of research work are terse. They often report just a test statistic and P-value. For example, the conclusion of Example 13.10 might be stated as "(t = —1.09, P = 0.2758)." Find the values of the one-sample ?: statistic needed to complete these
13.12 Job satisfaction; find the P-value. The P-value in Example 13.9 is the probahility(taking the null hypothesis /t = 0 to be true) that x takes a value at least as far from 0 as 17.(a) What is the sampling distribution of x when /x = 01 (Remember that the popula tion standard deviation is cr =
13.11 Sweetness loss in colas: find the P-value. The P-value for the first cola in Example 13.8 is the probability (taking the null hypothesis fx = Oto be true) that x takes a value at least as large as 0.3.(a) What is the sampling distribution of x when /t = 0? (Remember that the popula tion
13.10 Grading a teaching assistant. The examinations in a large accounting class are scaled after grading so that the mean score is 50. The professor thinks that one teaching assistant is a poor teacher and suspects that his students have a lower mean score than the class as a whole. The TA's
13.9 Measuring conductivity. State the null and alternative hypotheses for the study of electrical conductivity described in Exercise 13.7. (Is the alternative hypothesis one sided or two-sided?)
13.8 student attitudes. State the null and alternative hypotheses for the study of older students' attitudes described in Exercise 13.6. (Is the alternative hypothesis one-sided or two-sided?)
13.7 Measuring conductivity. The National Institute of Standards and Technology (NIST)supplies a "standard liciuid" whose electrical conductivity is supposed to be exactly 5. Is there reason to think that the true conductivity of a shipment of this liciuid is not 5?To find out, NIST measures the
13.6 Student attitudes. The Survey of Study Habits and Attitudes (SSHA) is a psycholog ical test that measures students' study habits and attitude toward school. Scores range from 0 to 200. The mean score for college students is about 115, and the standard devi ation is about 30. A teacher suspects
13.5 IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:'''114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93(a) These 31 girls are an SRS of all seventh-grade girls in the school
13.4 Measuring conductivity. The National Institute of Standards and Technology (NIST)supplies "standard materials" that have known properties. Here are 6 measurements of the electrical conductivity of the same standard liquid, which is supposed to have con ductivity 5:5.32 4.f 5.10 4.73 5.15 4.75
13.3 Find a critical value. The critical value z* for confidence level 97.5% is not in Table C.Use software or Table A of standard Normal probabilities to find z*. Include in your answer a sketch like Figure 13.2 with C = 0.975 aiad your critical value z* marked on the axis.
13.2 Explaining confidence. A student reads that a 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. Asked to explain the meaning of this interval, the student says, "95% of all young women have BMI between 26.2 and 27.4." Explain in simple language
13.1 Number skills of young men. The National Assessment of Educational Progress(NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age.^ Scores range from 0 to 500. The mean score for these 840 young men was x = 272. We want
12.38 The continuity correction. One reason why the Nor mal approximation may fail to give accurate estimates of bi nomial probabilities is that the binomial distributions are dis crete and the Normal distributions are continuous. That is, counts take only whole number values but Normal variables
12.37 A mixed group: probabilities. We would like to find the probability that exactly 2 of the 20 exposed children in the previous exercise develop whooping cough.(a) One way to get 2 infections is to get 1 among the 17 vacci nated children and 1 among the 3 unvaccinated children. Find the
12.36 A mixed group: means. A group of 20 children at a nursery school are exposed to whooping cough by playing with an infected child. Of these children 17 have been vaccinated and 3 have not.(a) What is the distribution of the number of new infections among the 17 vaccinated children? What is the
12.35 A whooping cough outbreak. In 2007, Bob Jones University ended its fall semester a week early because of a whooping cough outbreak; 158 students were isolated and an other 1200 given antibiotics as a precaution.^ Because the effect of childhood vaccination often wears off by late adoles
12.34 to 12.37 are based on this information.12.34 Vaccination at work. A group of 20 children at a nurs ery school are exposed to whooping cough by playing with an infected child.(a) If all 20 have been vaccinated, what is the mean number of new infections? What is the probability that no more
12.33 Is this coin balanced? While he was a prisoner of war during World War II, John Kerrich tossed a coin 10,000 times. He got 5067 heads. If the coin is perfectly balanced, the probability of a head is 0.5. Is there reason to think that Kerrich's coin was not balanced? To answer this question,
12.32 Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at ran dom from a universe of possible questions. (A strong student has a higher p than a weak student.) Answers to
12.31 Survey demographics. According to the Census Bu reau, 13% of American adults (age 18 and over) are Hispanic.An opinion poll plans to contact an SRS of 1200 adults.(a) What is the mean number of Hispanics in such samples?What is the standard deviation?(b) According to the 68-95-99.7 rule, what
12.30 High school dropouts In Canada. The high school dropout rate is lower in Canada than in the United States:among Canadians aged 20 to 24, 14% of men and 9% of women lack a high school diploma and are not attending school.'' A provincial "second chance system" mails a flyer to 25,000 young men
12.29 False positives in testing for HIV. A rapid test for the presence in the blood of antibodies to HIV, the virus that causes AIDS, gives a positive result with probability about 0.004 when a person who is free of HIV antibodies is tested. A clinic tests 1000 people who are all free of HIV
12.28 Genetics. According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio. That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent.(a) What is the
12.27 Hitting the fairway. One statistic used to assess pro fessional golfers is driving accuracy, the percent of drives that land in the fairway. Driving accuracy for PCA Tour profession als ranges from about 40% to about 75%. Tiger Woods hits the fairway about 60% of the time.'(a) Tiger hits 14
12.26 The pill, continued. A study of the effectiveness of oral contraceptives interviews a random sample of 500 women who are taking the pill.(a) Based on the information about typical use in Exercise 12.24, what is the probability that at least 25 of these women become pregnant in the next year?
12.25 On the Web, continued. A study of Internet usage in terviews a random sample of 500 men aged 18 to 34. Based on the information in Exercise 12.23, what is the probability that at least 235 of the men in the sample visit an online auction site at least once a month? (Check that the Normal
12.24 The pill. Many women take oral contraceptives to pre vent pregnancy. Under ideal conditions, 1% of women taking the pill become pregnant within one year. In typical use, how ever, 5% become pregnant.'' Choose at random 20 women tak ing the pill. How many become pregitant in the next year?(a)
12.23 On the Web. What kinds of Web sites do males aged 18 to 34 visit? About 50% of male Internet users in this age gtoiip visit an auction site such as eBay at least once a month.'Interview a random sample of 12 male Interiaet users aged 18 to 34-(a) What is the distribution of the number who

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