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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
16.10 Survival times in a medical study. The “survival times” of machines before a breakdown and of cancer patients after treatment are typically strongly right-skewed. Table 1.8 (page 29) gives the survival times (in days) of 72 guinea pigs in a medical trial.5(a) Make a histogram of the
16.9 Standard error versus the bootstrap standard error. We have two ways to estimate the standard deviation of a sample mean x: use the formula s/√n for the standard error, or use the bootstrap standard error.(a) Find the sample standard deviation s for the 60 IQ test scores in Exercise 16.4 and
16.8 Bootstrap distribution of average audio file length. The distribution of the lengths (in seconds)of audio files found on an iPod (Table 7.3, page 436) is skewed. We previously transformed the data prior to using t procedures.
16.7 Bootstrap distribution of average C-reactive protein. The measurements of C-reactive protein in 40 children (Exercise 7.26, page 442) are very strongly skewed. We were hesitant to use t procedures for inference from these data.
16.6 Bootstrap distribution of average listening time. The numbers of hours per month listening to full-track music on cell phones in a random sample of 8 U.S. 3G subscribers (Example 7.1, page 421)are 5 6 0 4 11 9 2 3 The distribution has no outliers, but we cannot assess Normality from so small a
16.5 Bootstrap distribution of average CO2 emissions. The distribution of carbon dioxide(CO2) emissions in Table 1.6 (page 26) is strongly skewed to the right. The United States and several other countries appear to be high outliers.
16.4 Bootstrap distribution of average IQ score. The distribution of the 60 IQ test scores in Table 1.3(page 13) is roughly Normal (see Figure 1.7) and the sample size is large enough that we expect a Normal sampling distribution.
16.3 What’s wrong? Explain what is wrong with each of the following statements.(a) The bootstrap distribution is created by resampling with replacement from the population.(b) The bootstrap distribution is created by resampling without replacement from the original sample.(c) When generating the
16.2 Standard deviation versus standard error. Explain the difference between the standard deviation of a sample and the standard error of a statistic such as the sample mean.
16.1 A small bootstrap example. To illustrate the bootstrap procedure, let’s bootstrap a small random subset of the Verizon data:26.47 0.00 5.32 17.30 29.78 3.67(a) Sample with replacement from this initial SRS by rolling a die.Rolling a 1 means select the first member of the SRS (26.47), a 2
15.48 CHALLENG E Multiple comparisons for the turkeyprocessing plant. Exercise 15.47 outlines how to use the Wilcoxon rank sum test several times for multiple comparisons with overall significance level 0.05 for all comparisons together.In Exercise 15.42 you found that the airborne fungus spore
15.47 CHALLENGE Multiple comparisons for plants and hummingbirds. As in ANOVA, we often want to carry out a multiple-comparisons procedure following a Kruskal-Wallis test to tell us which groups differ significantly.29 Here is a simple method: If we carry out k tests at fixed significance level
15.46 Iron in food cooked in iron pots. The data show that food cooked in iron pots has the highest iron content. They also suggest that the three types of food differ in iron content. Is there significant evidence that the three types of food differ in iron content when all are cooked in iron pots?
15.45 Cooking meat and legumes in aluminum and clay pots. There appears to be little difference between the iron content of food cooked in aluminum pots and food cooked in clay pots. Is there a significant difference between the iron content of meat cooked in aluminum and clay?Is the difference
15.44 Cooking vegetables in different pots. Does the vegetable dish vary in iron content when cooked in aluminum, clay, and iron pots?(a) What do the data appear to show? Check the conditions for one-way ANOVA. Which requirements are a bit dubious in this setting?(b) Instead of ANOVA, do a rank
15.43 CHALLENGE Plants and hummingbirds. Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.Over time, the lengths of the flowers and the form of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in
15.42 Air in a turkey-processing plant. The air in poultry-processing plants often contains fungus spores. If the ventilation is inadequate, this can affect the health of the workers. To measure the presence of spores, air samples are pumped to an agar plate and “colony-forming units (CFUs)”
15.41 Selling prices of three- and four-bedroom homes. Exercise 7.141 (page 486) reports data on the selling prices of 9 four-bedroom houses and 28 three-bedroom houses in West Lafayette, Indiana.We wonder if there is a difference between the average prices of three- and four-bedroom houses in this
15.40 Response times for telephone repair calls.Exercise 16.55 (page 16-53) presents data on the time required for the telephone company Verizon to respond to repair calls from its own customers and from customers of a CLEC, another phone company that pays Verizon to use its local lines.Here are
15.39 Heart disease and smoking. In a study of heart disease in male federal employees, researchers classified 356 volunteer subjects according to their socioeconomic status (SES) and their smoking habits. There were three categories of SES: high, middle, and low. Individuals were asked whether
15.38 Logging in Borneo. In Exercise 15.13 you compared the number of tree species in plots of land in a tropical rainforest that had never been logged with similar plots nearby that had been logged 8 years earlier. The researchers also counted species in plots that had been logged just 1 year
15.37 Food safety. Example 15.6 describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. The full data set is available on the text CD and Web site as the file eg15 006. It contains the responses of 303 people to several questions.
15.36 Decay of polyester fabric in landfills. Here are the breaking strengths (in pounds) of strips of polyester fabric buried in the ground for several lengths of time:23 Time Breaking strength 2 weeks 118 126 126 120 129 4 weeks 130 120 114 126 128 8 weeks 122 136 128 146 140 16 weeks 124 98 110
15.35 Do the calculations by hand. Exercise 15.34 gives data on the counts of insects attracted by boards of four different colors. Carry out the Kruskal-Wallis test by hand, following these steps.(a) What are I, the ni, and N?(b) Arrange the counts in order and assign ranks.Be careful about ties.
15.34 Detecting insects in farm fields. To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and examine the insects trapped on the boards.Which colors attract insects best? Experimenters placed six boards of each of four colors at random
15.33 Jumping and strong bones. Many studies suggest that exercise causes bones to get stronger. One study examined the effect of jumping on the bone density of growing rats. Ten rats were assigned to each of three treatments: a 60-centimeter “high jump,” a 30-centimeter “low jump,” and a
15.32 Vitamins in bread. Does bread lose its vitamins when stored? Here are data on the vitamin C content (milligrams per 100 grams of flour) in bread baked from the same recipe and stored for 1, 3, 5, or 7 days.20 The 10 observations are from 10 different loaves of bread.Condition Vitamin C
15.31 Weight gains with an extra 1000 calories per day. Exercise 7.32 (page 444) presents these data on the weight gains (in kilograms) of adults who were fed an extra 1000 calories per day for 8 weeks:18 Weight Subject Before After 1 55.7 61.7 2 54.9 58.8 3 59.6 66.0 4 62.3 66.2 5 74.2 79.0 6 75.6
15.30 Vitamin C in wheat-soy blend. The U.S.Agency for International Development provides large quantities of wheat-soy blend (WSB) for development programs and emergency relief in countries throughout the world. One study collected data on the vitamin C content of 27 bags of WSB at the factory and
15.29 Radon detectors. How accurate are radon detectors of a type sold to homeowners? To answer this question, university researchers placed 12 detectors in a chamber that exposed them to 105 picocuries per liter (pCi/l) of radon.16 The detector readings are as follows:91.9 97.8 111.4 122.3 105.4
15.28 Use of latex gloves by nurses. How often do nurses use latex gloves during procedures for which glove use is recommended? A matched pairs study observed nurses (without their knowledge)before and after a presentation on the importance of glove use. Here are the proportions of procedures for
15.27 Food safety. Example 15.6 describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. The full data set is available on the text CD and Web site as the file eg15 006. It contains the responses of 303 people to several questions.
15.26 A summer language institute for teachers. A matched pairs study of the effect of a summer language institute on the ability of teachers to comprehend spoken French had these improvements in scores between the pretest and the posttest for 20 teachers:2 0 6 6 3 3 2 3 −6 6 6 6 3 0 1 1 0 2 3 3
15.25 The full moon and behavior. Can the full moon influence behavior? A study observed 15 nursinghome patients with dementia. The number of incidents of aggressive behavior was recorded each day for 12 weeks. Call a day a “moon day” if it is the day of a full moon or the day before or after a
15.24 Compare exercise at a medium rate with exercise at a low rate. Do the data from the previous exercise give good reason to think that stepping at the medium rate increases heart rates more than stepping at the low rate?(a) State hypotheses in terms of comparing the median increases for the two
15.23 Heart rate and exercise. A student project asked subjects to step up and down for three minutes and measured their heart rates before and after the exercise. Here are data for five subjects and two treatments: stepping at a low rate (14 steps per minute) and at a medium rate (21 steps per
15.22 Carbon dioxide and plant growth. The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers
15.21 Significance test for lower-ranked spas. Refer to Exercise 15.19.Find μW+, σW+, and the Normal approximation for the P-value for the Wilcoxon signed rank test.
15.20 Significance test for top-ranked spas. Refer to Exercise 15.18.Find μW+, σW+, and the Normal approximation for the P-value for the Wilcoxon signed rank test.
15.19 Scores for lower-ranked spas. Refer to the previous exercise. Here are the scores for a random sample of 7 spas that ranked between 19 and 36:Spa 1 2 3 4 5 6 7 Diet/Cuisine 77.3 85.7 84.2 85.3 83.7 84.6 78.5 Program/Facilities 95.7 78.0 87.2 85.3 93.6 76.0 86.3 Answer the questions from the
15.18 Services provided by top spas. The readers’ poll in Cond´e Nast Traveler magazine that ranked 36 top resort spas and that was described in Exercise 15.1 also reported scores on Diet/Cuisine and on Program/Facilities. Here are the scores for a random sample of 7 spas that ranked in the top
15.17 Attitudes toward secondhand stores. To study customers’ attitudes toward secondhand stores, researchers interviewed samples of shoppers at two secondhand stores of the same chain in two cities. Here are data on the incomes of shoppers at the two stores, presented as a two-way table of
15.16 Compare fairs with restaurants. The data file used in Example 15.6 and Exercise 15.15 contains 303 rows, one for each of the 303 respondents.Each row contains the responses of one person to several questions. We wonder if people are more concerned about the safety of food served at fairs than
15.15 Food safety. Example 15.12 describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. The full data set with the responses of 300 people to several questions is in the file eg15 012. The variables in this data set are (in
15.14 Improved methods for teaching reading. Do new “directed reading activities” improve the reading ability of elementary school students, as measured by their Degree of Reading Power (DRP)score? A study assigns students at random to either the new method (treatment group, 21 students) or
15.13 Effects of logging in Borneo. “Conservationists have despaired over destruction of tropical rainforest by logging, clearing, and burning.”These words begin a report on a statistical study of the effects of logging in Borneo.8 Here are data on the number of tree species in 12 unlogged
15.12 Learning math through subliminal messages.A “subliminal” message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of students who had failed the mathematics part of the City University of New York Skills
15.11 Decay of polyester fabrics in landfills. How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to
15.10 Weeds and corn yield. The corn yield study of Example 15.1 also examined yields in four plots having 9 lamb’s-quarter plants per meter of row.The yields (bushels per acre) in these plots were 162.8 142.4 162.7 162.4 There is a clear outlier, but rechecking the results found that this is the
15.9 Do the calculations by hand. Use the data in Exercise 15.7 for children telling Story 2 to carry out by hand the steps in the Wilcoxon rank sum test.(a) Arrange the 10 observations in order and assign ranks. There are no ties.(b) Find the rank sum W for the five high-progress readers. What are
15.8 Repeat the analysis for Story 2. Repeat the analysis of Exercise 15.7 for the scores when children retell a story they have heard and seen illustrated with pictures (Story 2).
15.7 Storytelling and the use of language. A study of early childhood education asked kindergarten students to retell two fairy tales that had been read to them earlier in the week. The 10 children in the study included 5 high-progress readers and 5 low-progress readers. Each child told two
15.6 The effect of Spa Bellagio on the P-value. Refer to Exercises 15.2 and 15.4. Answer the questions for Exercise 15.5 using the altered data.
15.5 The P-value for top spas. Refer to Exercises 15.1 and 15.3. Find μW,σW, and the standardized rank sum statistic. Then give an approximate P-value using the Normal approximation. What do you conclude?
15.4 Effect of Spa Bellagio on the test statistic. Refer to Exercise 15.2.Using the altered data, state appropriate null and alternative hypotheses and calculate the value of W, the test statistic.
15.3 Hypotheses and test statistic for top spas. Refer to Exercise 15.1.State appropriate null and alternative hypotheses for this setting and calculate the value of W, the test statistic.
15.2 The effect of Spa Bellagio on the result. Refer to the previous exercise.Spa Bellagio in Las Vegas is one of the spas in Group B. Suppose this spa had been the second spa selected in the random sample for Group B. Replace the observation 780 in Group B by 4003, the number of rooms in Spa
15.1 Numbers of rooms in top spas. A report of a readers’ poll in Cond´e Nast Traveler magazine ranked 36 top resort spas.2 Let Group A be the top-ranked 18 spas, and let Group B be the next 18 rated spas in the list. A simple random sample of size 5 was taken from each group, and the number of
14.43 CHALLENGE An example of Simpson’s paradox. Here is an example of Simpson’s paradox, the reversal of the direction of a comparison or an association when data from several groups are combined to form a single group. The data concern two hospitals, A and B, and whether or not patients
14.42 CHALLENGE Is there an effect of gender? In this exercise we investigate the effect of gender on the odds of getting a high GPA.(a) Use gender to predict HIGPA using a logistic regression. Summarize the results.(b) Perform a logistic regression using gender and the two SAT scores to predict
14.41 CHALLENGE Use high school grades and SAT scores to predict high grade point averages.Run a logistic regression to predict HIGPA using the three high school grade summaries and the two SAT scores as explanatory variables. We want to produce an analysis that is similar to that done for the case
14.40 CHALLENGE Use SAT scores to predict high grade point averages. Use a logistic regression to predict HIGPA using the two SAT scores as explanatory variables.(a) Summarize the results of the hypothesis test that the coefficients for both explanatory variables are zero.(b) Give the coefficient
14.39 CHALLENGE Use high school grades to predict high grade point averages. Use a logistic regression to predict HIGPA using the three high school grade summaries as explanatory variables.(a) Summarize the results of the hypothesis test that the coefficients for all three explanatory variables are
14.38 CHALLENGE Compare the analyses. For the cheese data analyzed in Examples 14.9, 14.10, and the two exercises above, there are three explanatory variables. There are three different logistic regressions that include two explanatory variables. Run these. Summarize the results of these analyses,
14.37 What about lactic acid? Refer to the previous exercise. Run the same analysis using Lactic as the explanatory variable.
14.36 The amount of acetic acid predicts the taste of cheese. In Examples 14.5 and 14.9, we analyzed data from the CHEESE data set described in the Data Appendix. In those examples, we used Acetic as the explanatory variable. Run the same analysis using H2S as the explanatory variable.
14.35 Alcohol use and bicycle accidents. A study of alcohol use and deaths due to bicycle accidents collected data on a large number of fatal accidents.10 For each of these, the individual who died was classified according to whether or not there was a positive test for alcohol and by gender. Here
14.34 Income level of customers. The study mentioned in the previous exercise also asked about income.Among Internet users, 493 reported income of less than $50,000 and 378 reported income of$50,000 or more. (Not everyone answered the income question.) The corresponding numbers for nonusers were
Education level of customers. To devise effective marketing strategies it is helpful to know the characteristics of your customers. A study compared demographic characteristics of people who use the Internet for travel arrangements and of people who do not.9 Of 1132 Internet users, 643 had
14.32 Repair times for golf clubs. The Ping Company makes custom-built golf clubs and competes in the $4 billion golf equipment industry. To improve its business processes, Ping decided to seek ISO 9001 certification.8 As part of this process, a study of the time it took to repair golf clubs sent
14.31 Reducing the number of workers. To be competitive in global markets, many corporations are undertaking major reorganizations. Often these involve “downsizing” or a “reduction in force” (RIF), where substantial numbers of employees are terminated. Federal and various state laws require
14.30 Gender bias in syntax textbooks. The gender bias in syntax textbooks is described in the log odds scale in Exercise 14.28.(a) Transform the slope to the odds and the 95% confidence interval for the slope to a 95%confidence interval for the odds.(b) Write a conclusion using the odds to
14.29 High blood pressure and cardiovascular disease. The results describing the relationship between blood pressure and cardiovascular disease are given in terms of the change in log odds in Exercise 14.27.(a) Transform the slope to the odds and the 95% confidence interval for the slope to a
14.28 Gender bias in syntax textbooks. The data from the study of gender bias in syntax textbooks given in Exercise 14.26 are analyzed using logistic regression. The estimated slope is b1 = 1.8171 and its standard error is SEb1= 0.3686.(a) Give a 95% confidence interval for the slope.(b) Calculate
14.27 High blood pressure and cardiovascular disease. Refer to the study of cardiovascular disease and blood pressure in Exercise 14.25.Computer output for a logistic regression analysis of these data gives the estimated slope b1 = 0.7505 with standard error SEb1= 0.2578.(a) Give a 95% confidence
14.26 Gender bias in syntax textbooks. To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts.7 One part of the study examined the use of the words“girl,” “boy,” “man,” and
14.25 High blood pressure and cardiovascular disease. There is much evidence that high blood pressure is associated with increased risk of death from cardiovascular disease. A major study of this association examined 3338 men with high blood pressure and 2676 men with low blood pressure.During the
14.24 High-tech companies and stock options.Refer to Exercises 14.21 to 14.23. Repeat the calculations assuming that you have twice as many observations with the same proportions. In other words, assume that there are 182 high-tech firms and 218 non-high-tech firms. The numbers of firms offering
14.23 High-tech companies and stock options. Refer to Exercises 14.21 and 14.23. Software gives 0.3347 for the standard error of b1.(a) Find the 95% confidence interval for β1.(b) Transform your interval in (a) to a 95%confidence interval for the odds ratio.(c) What do you conclude?
14.22 High-tech companies and stock options. Refer to the previous exercise.(a) Find the log odds for the high-tech firms. Do the same for the non-high-tech firms.(b) Define an explanatory variable x to have the value 1 for high-tech firms and 0 for non-high-tech firms. For the logistic model, we
14.21 High-tech companies and stock options.Different kinds of companies compensate their key employees in different ways. Established companies may pay higher salaries, while new companies may offer stock options that will be valuable if the company succeeds. Do high-tech companies tend to offer
14.20 What purchases will be made? A poll of 811 adults aged 18 or older asked about purchases that they intended to make for the upcoming holiday season.5 One of the questions asked what kind of gift they intended to buy for the person on whom they intended to spend the most. Clothing was the
14.19 Interpret the odds ratios. Refer to the previous exercise. The researchers also reported odds ratios with 95% confidence intervals for this logistic regression model. Here is a summary:95% Confidence Limits Explanatory variable Odds ratio Lower Upper Reader age 1.65 1.27 2.16 Model gender
14.18 Sexual imagery in magazine ads. Exercise 9.18(page 551) presents some results of a study about how advertisers use sexual imagery to appeal to young people. The clothing worn by the model in each of 1509 ads was classified as “not sexual”or “sexual” based on a standardized criterion.A
14.17 CHALLEN GE z and the X2 statistic. The Minitab output in Figure 14.5 does not give the value of X2. The column labeled “Z” provides similar information.(a) Find the value under the heading “Z” for the predictor lconc. Verify that Z is simply the estimated coefficient divided by its
14.16 Give a 99% confidence interval for the odds ratio. Refer to Example 14.8 and the outputs in Figure 14.5. Using the estimate b1 and its standard error, find the 95% confidence interval for the odds ratio and verify that this agrees with the interval given by the software.
14.15 Give a 99% confidence interval for β1. Refer to Example 14.8. Suppose that you wanted to report a 99% confidence interval for β1. Show how you would use the information provided in the outputs shown in Figure 14.5 to compute this interval.
14.14 CHALLENGE Interpret the fitted model. If we apply the exponential function to the fitted model in Example 14.9, we get odds = e−13.71+2.25x = e−13.71 × e2.25x Show that, for any value of the quantitative explanatory variable x, the odds ratio for increasing x by 1, oddsx+1 oddsx is e2.25
14.13 “No Sweat” labels on clothing. Refer to Exercise 14.11. Use x = 1 forwomen and x = 0 for men.(a) Find the estimates b0 and b1.(b) Give the fitted logistic regression model.(c) What is the odds ratio for women versus men?
14.12 Exclusive territories for franchises. Refer to Exercise 14.10. Use x = 1 for the exclusive territories and x = 0 for the other territories.(a) Find the estimates b0 and b1.(b) Give the fitted logistic regression model.(c) What is the odds ratio for exclusive territory versus no exclusive
14.11 “No Sweat” labels on clothing. Following complaints about the working conditions in some apparel factories both in the United States and abroad, a joint government and industry commission recommended in 1998 that companies that monitor and enforce proper standards be allowed to display a
14.10 Find the logistic regression equation and the odds ratio. A study of 170 franchise firms classified each firm as to whether it was successful or not and whether or not it had an exclusive territory.3 Here are the data:Observed numbers of firms Exclusive territory Success Yes No Total Yes 108
14.9 What’s wrong? For each of the following, explain what is wrong and why.(a) For a multiple logistic regression with 6 explanatory variables, the null hypothesis that the regression coefficients of all of the explanatory variables are zero is tested with an F test.(b) In logistic regression
14.8 Find the logistic regression equation and the odds ratio. Refer to Exercises 14.4 and 14.6. Find the logistic regression equation and the odds ratio.
14.7 Find the logistic regression equation and the odds ratio. Refer to Exercises 14.3 and 14.5. Find the logistic regression equation and the odds ratio.
14.6 Find the odds. Refer to Exercise 14.4. Find the log odds for the men and the log odds for the women.
14.5 Find the odds. Refer to Exercise 14.3. Find the log odds for the men and the log odds for the women.
14.4 Find the odds. Refer to the previous exercise. Find the odds of selecting Commercial B for the men. Do the same for the women.
14.3 Energy drink commercials. A study was designed to compare two energy drink commercials. Each participant was shown the commercials, A and B, in random order and asked to select the better one.There were 100 women and 140 men who participated in the study.Commercial A was selected by 45 women
14.2 Given the odds, find the probability. If you know the odds, you can find the probability by solving the equation for odds given above for the probability. So, ˆp = odds/(odds + 1). If the odds of an outcome are 2 (or 2 to 1), what is the probability of the outcome?
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