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Elementary Statistics 10th Edition Mario F. Triola - Solutions

Deaths from Motor Vehicles and Murders Listed below are the number of motor vehicle deaths (in hundreds) and the number of murders (in hundreds) in the United States for each of several different years. Test for a correlation between those two variables.Motor vehicle deaths 435 410 418 425 434 436
Crickets and Temperature The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The Song of Insects by George W. Pierce,
Correlation Between Salary and Physical Demand Exercise 11 includes paired salary and stress level ranks for 10 randomly selected jobs. The physical demands of the jobs were also ranked; the salary and physical demand ranks are given below (based on data from The Jobs Rated Almanac). Does there
Sunspots and Super Bowl Points For a recent series of 10 years, the sunspot numbers and the total points scored in the Super Bowl were obtained. The table below lists the ranks of each set of values. Test for a correlation between sunspot number and Super Bowl points. Does the result agree with
Efficiency Refer to Table 13-2 and identify the efficiency of the rank correlation test.What does that value tell us about the test?
Notation We represent the rank correlation coefficient test statistic with the notation rs, and the corresponding population parameter is represented as rs. Why is the subscript s used? Does the subscript s represent the same standard deviation s introduced in Section 3-3?
Rank Correlation If two judges each rank 25 different gymnasts from 1 through 25 with no ties, and their rankings agree perfectly, what is the value of the rank correlation coefficient?
Rank Correlation What major advantage does the rank correlation method of this section have over the linear correlation method of Section 10-2?
Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by For each group of tied observations in the combined set of all sample data, calculate T 5 t3 2 t, where t is the number of
13 in Appendix B. At the 0.05 significance level, test the claim that the median weights of M&Ms are the same for each of the six different color populations. If it is the intent of Mars, Inc. to make the candies so that the different color populations are the same, do your results suggest that the
11. Appendix B Data Set: Weights of Pennies Refer to Data Set 14 in Appendix B and use the weights of the Indian pennies, wheat pennies, pre-1983 pennies, and post-1983 pennies. Use a 0.05 significance level to test the claim that the median weight of pennies is the same for the four different
10. Laboratory Testing of Flammability of Children’s Sleepwear Flammability tests were conducted on children’s sleepwear. The Vertical Semirestrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion
9. Exercise and Stress A study was conducted to investigate the effects of exercise on stress. The table below lists systolic blood pressure readings (in mmHg) of subjects from the time preceding 25 minutes of aerobic bicycle exercise and preceding the introduction of stress through arithmetic and
8. Testing for Skull-Breadth Differences in Different Times The accompanying values are measured maximum breadths of male Egyptian skulls from different epochs(based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver). Changes in head shape over time suggest that
7. Is Solar Energy the Same Every Day? A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table.Use a 0.05 significance level to test the
6. Does the Weight of a Car Affect Chest Injuries in a Crash? Data were obtained from car crash experiments conducted by the National Transportation Safety Administration.New cars were purchased and crashed into a fixed barrier at 35 mi/h, and the chest deceleration data (g) are given below. Use
5. Does the Weight of a Car Affect Head Injuries in a Crash? Data were obtained from car crash experiments conducted by the National Transportation Safety Administration.New cars were purchased and crashed into a fixed barrier at 35 mi/h, and measurements were recorded for the dummy in the
4. Requirements Fifty families are randomly selected and IQ tests are given to the mother, father, and firstborn child. Can the Kruskal-Wallis test be used to test the claim that the three populations of mothers, fathers, and firstborn children have IQ scores with the same median? Why or why
3. Efficiency Refer to Table 13-2 and identify the efficiency of the Kruskal-Wallis test.What does that value tell us about the test?
2. Kruskal-Wallis Test If the Kruskal-Wallis test and one-way analysis of variance are both used with three sets of independent samples, will both tests always result in the same conclusion?
1. Kruskal-Wallis Test What major advantage does the Kruskal-Wallis test have over the one-way analysis of variance test?
14. Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the test statistic given in this section because both sample sizes do not exceed 10.a.
12. Appendix B Large Data Set: Weights of Pennies Refer to Data Set 14 in Appendix B and use the weights of the wheat pennies and the weights of the pre-1983 pennies.Use a 0.05 significance level to test the claim that those two samples are from populations with the same median.
11. Appendix B Large Data Set: Pulse Rates Repeat Exercise 10 using all 40 pulse rates of men and all 40 pulse rates of women.
9. Hypothesis Test for Difference in Car Taxi Ages When the author visited Dublin in Ireland, he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages (in years) are listed below. Use a 0.05 significance level to test the claim that there is a difference
8. Testing the Anchoring Effect Randomly selected statistics students were given 5 sec to estimate the value of a product of numbers with the results given in the accompanying table. (See the Cooperative Group Activities at the end of Chapter 3.) Do the samples appear to be significantly
7. Are Severe Psychiatric Disorders Related to Biological Factors? One study used x-ray computed tomography (CT) to collect data on brain volumes for a group of patients with obsessive-compulsive disorders and a control group of healthy persons.The accompanying list shows sample results (in
4. Efficiency Refer to Table 13-2 and identify the efficiency of the Wilcoxon rank-sum test. What does that value tell us about the test?
3. Wilcoxon Rank-Sum Test The Wilcoxon rank-sum test and the methods of hypothesis testing described in Section 9-3 both apply to two independent samples. What advantage does the Wilcoxon rank-sum test have over the test described in Section 9-3?
2. Wilcoxon Rank-Sum Test The test statistic for the Wilcoxon rank-sum test is based on the rank sum R, which has a distribution that is approximately normal. Is the Wilcoxon rank-sum test a parametric test because it requires a normal distribution?
1. Wilcoxon Rank-Sum Test What is the most fundamental difference between the Wilcoxon signed-ranks test and the Wilcoxon rank-sum test?
12. Testing for Difference Between Times Depicting Alcohol Use and Tobacco Use Refer to Data Set 5 in Appendix B. Use only those movies that showed some use of tobacco or alcohol. (That is, ignore those movies with times of zero for both tobacco use and alcohol use.) Does there appear to be a
11. Testing for Difference Between Forecast and Actual Temperatures Refer to Data Set 8 in Appendix B and use the actual high temperatures and the three-day forecast high temperatures. Does there appear to be a difference?
4. Wilcoxon Signed-Ranks Test A market researcher designs an experiment that involves a survey of married couples in randomly selected shopping malls. After separating the male and female, each spouse is asked how much has been spent shopping in the past hour. The results are analyzed with the
3. Wilcoxon Signed-Ranks Test Given sample data consisting of matched pairs, we can compare the values using the sign test or the Wilcoxon signed-ranks test. What important advantage does the Wilcoxon signed-ranks test have over the sign test?
2. Wilcoxon Signed-Ranks Test and Sign Test The Wilcoxon signed-ranks test and the sign test can both be used with sample data consisting of matched pairs. Could they both lead to the same conclusion? Do they both always lead to the same conclusion?
1. Wilcoxon Signed-Ranks Test Why would we use the Wilcoxon signed-ranks test for matched pairs instead of the methods presented in Section 9-4?
21. Normal Approximation Error The Compulife.com company has hired 18 women among the last 54 new employees. Job applicants are about half men and half women, all of whom are qualified. Using a 0.01 significance level with the sign test, is there sufficient evidence to charge bias? Does the
20. Finding Critical Values Table A-7 lists critical values for limited choices ofa. Use Table A-1 to add a new column in Table A-7 (down to n 5 15) that represents a significance level of 0.03 in one tail or 0.06 in two tails. For any particular n, use p 5 0.5, because the sign test requires the
19. Procedures for Handling Ties In the sign test procedure described in this section, we excluded ties (represented by 0 instead of a sign of 1or 2). Asecond approach is to treat half of the 0s as positive signs and half as negative signs. (If the number of 0s is odd, exclude one so that they can
18. Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone their death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, 6062 deaths were recorded in the week before Thanksgiving, and there were 5938 deaths
17. Nominal Data: Travel Through the Internet Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for
16. Nominal Data: Car Crashes In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home (based on data from Progressive Insurance).Use a 0.01 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home. Are the results
15. Nominal Data: Gender Selection for Boys The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As this book was being written, 51 babies were born to parents using the YSORT method, and 39 of them were boys. Use
14. Testing for Median Weight of Quarters Listed below are weights (in grams) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use a 0.05 significance level to test the claim that the median is equal to 5.670 g. Do quarters
13. Testing for a Median Body Temperature of 98.6°F A premed student in a statistics class is required to do a class project. Intrigued by the body temperatures in Data Set 2 of 688 Chapter 13 Nonparametric Statistics Appendix B, she plans to collect her own sample data to test the claim that the
12. Heights of Winners and Runners-Up Listed below are the heights of candidates who won presidential elections and the heights of the candidates with the next highest number of popular votes. The data are in chronological order, so the corresponding heights from the two lists are matched. For
11. Testing for a Difference Between Reported and Measured Male Heights As part of the National Health Examination Survey conducted by the Department of Health and Human Services, self-reported heights and measured heights were obtained for males aged 12–16. Listed below are sample results. Is
Efficiency of the Sign Test Refer to Table 13-2 and identify the efficiency of the sign test. What does that value tell us about the sign test?
Sign Test Procedure You have been given the task of testing the claim that a method of gender selection has the effect of increasing the likelihood that a baby will be a girl, and sample data consist of 20 girls among 80 newborn babies. Without applying the formal sign test procedure, what do you
Sign Test Why is the procedure introduced in this section referred to as the “sign” test?
Nonparametric Test Why is the sign test considered to be a “nonparametric” test or a“distribution-free” test?
Does an interaction between gender and major have an effect on wristwatch accuracy?
Does major have an effect on wristwatch accuracy?
Does gender appear to have an effect on the accuracy of the wristwatch?
Is there sufficient evidence to reject equality of the mean estimates for different majors? Describe how the majors were categorized.
2. In-class activity Begin by asking each student in the class to estimate the length of the classroom. Specify that the length is the distance between the chalkboard and the opposite wall. (See Review Exercises 3–5.) On the same sheet of paper, each student should also write his or her gender
1. Out-of-class activity The World Almanac and Book of Facts includes a section called “Noted Personalities,”with subsections comprised of architects, artists, business leaders, cartoonists, social scientists, military leaders, philosophers, political leaders, scientists, writers, composers,
4. Weights of Babies: Finding Probabilities In the United States, weights of newborn babies are normally distributed with a mean of 7.54 lb and a standard deviation of 1.09 lb(based on data from “Birth Weight and Perinatal Mortality,” by Wilcox, Skjaerven, Buekens, and Kiely, Journal of the
3. Blue Genes Some couples have genetic characteristics configured so that one-quarter of all their offspring have blue eyes. A study is conducted of 100 couples believed to have those characteristics, with the result that 19 of their 100 offspring have blue eyes. Assuming that one-quarter of all
2. M&M Treatment The table below lists 60 SAT scores separated into categories according to the color of the M&M candy used as a treatment. The SAT scores are based on data from the College Board, and the M&M color element is based on author whimsy.a. Find the mean of the 20 SAT scores in each of
1. Longevity Refer to the numbers of years that U.S. presidents and popes and British monarchs lived after their inauguration, election, or coronation. The data are listed in the table used for Review Exercise 8.a. Find the mean for each of the three groups.b. Find the standard deviation for each
7. Auto Pollution The accompanying table lists the amounts of greenhouse gases emitted by different cars in one year.a. Assuming that there is no interaction effect, is there sufficient evidence to support the claim that amounts of emitted greenhouse gases are affected by the type of transmission
6. Smoking, Body Temperature, Gender The table below lists body temperatures obtained from randomly selected subjects (based on Data Set 2 in Appendix B). The temperatures are categorized according to gender and whether the subject smokes. Using a 0.05 significance level, test for an interaction
5. Effect of Major Assume that estimated lengths are not affected by an interaction between gender and major. Is there sufficient evidence to support the claim that estimated length is affected by major?
4. Effect of Gender Assume that estimated lengths are not affected by an interaction between gender and major. Is there sufficient evidence to support the claim that estimated length is affected by gender?
3. Interaction Effect Test the null hypothesis that the estimated lengths are not affected by an interaction between gender and major.
2. Readability Scores Listed below are Flesch Reading Ease scores from each of 12 randomly selected pages in Tom Clancy’s The Bear and the Dragon, J. K. Rowling’s Harry Potter and the Sorcerer’s Stone, and Leo Tolstoy’s War and Peace. Use a 0.05 significance level to test the claim that the
1. Interpreting Computer Display: Drinking and Driving The Associated Insurance Institute sponsors studies of the effects of drinking on driving. In one such study, three groups of adult men were randomly selected for an experiment designed to measure their blood alcohol levels after consuming five
4. Two-Way ANOVA A geneticist collects data consisting of eye colors, and the colors are categorized by gender (male, female) and age bracket (under 30, 30 and older).Can the methods of this chapter be used to test for effects of gender and age bracket on eye color? Why or why not?
3. Which Test? Assume that the clinical trial in Exercise 2 is modified to exclude the treatment consisting of 20 mg of the drug. What method should be used to test for equality of the mean amounts of cholesterol reductions in the placebo group and the 10-mg treatment group?
2. Which Test? A medical researcher conducts a clinical trial of a drug intended to reduce LDL cholesterol. Fifty subjects are given 10 mg of the drug, 50 other subjects are given 20 mg of the drug, and 50 other subjects are given a placebo. What method should be used to test for equality of the
1. Analysis of Variance Why is the method used to test equality of three or more population means referred to as analysis of “variance,” when means are the parameters of interest?
15. Transformations of Data Assume that two-way ANOVA is used to analyze sample data consisting of more than one entry per cell. How are the ANOVA results affected in each of the following cases?a. The same constant is added to each sample value.b. Each sample value is multiplied by the same
14. Marathon Times Listed below are New York Marathon running times (in seconds)for randomly selected runners who completed the marathon. Are the running times 664 Chapter 12 Analysis of Variance affected by an interaction between gender and age bracket? Are running times affected by gender? Are
13. Pulse Rates The following table lists pulse rates from Data Set 1 in Appendix B. Are pulse rates affected by an interaction between gender and age? Are pulse rates affected by gender? Are pulse rates affected by age?>Minitab>>>Age Under 20 20–40 Over 40 Male 96 64 68 60 64 88 72 64 68 72 60
12. Hearing Tests: Effect of Word List Assuming that there is no effect on hearing test scores from an interaction between subject and list, is there sufficient evidence to support the claim that the choice of word list has an effect on the hearing test score?In Exercises 13 and 14, use software or
11. Hearing Tests: Effect of Subject Assuming that there is no effect on hearing test scores from an interaction between subject and list, is there sufficient evidence to support the claim that the choice of subject has an effect on the hearing test score? Interpret the result by explaining why it
10. Effect of Type of SAT Test Assume that SAT scores are not affected by an interaction between gender and the type of test (verbal math). Is there sufficient evidence to support the claim that the type of test (verbal math) has an effect on SAT scores?
9. Effect of Gender Assume that SAT scores are not affected by an interaction between gender and the type of test (verbal math). Is there sufficient evidence to support the claim that gender has an effect on SAT scores?
8. Interaction Effect Test the null hypothesis that SAT scores are not affected by an interaction between gender and test (verbal>math). What do you conclude?
7. Effect of Treatment Refer to the Minitab display and assume that the weights of poplar trees are not affected by an interaction between site and treatment. Is there sufficient evidence to support the claim that treatment has an effect on weight?
6. Effect of Site Refer to the Minitab display and assume that the weights of poplar trees are not affected by an interaction between site and treatment. Is there sufficient evidence to support the claim that site has an effect on weight?
5. Interaction Effect Refer to the Minitab display and test the null hypothesis that the weights of poplar trees are not affected by an interaction between site and treatment.What do you conclude?
4. Interaction Shown below is a Minitab-generated interaction plot similar in nature to Figure 12-3. [Like Figure 12-3, this interaction plot is based on weights of trees, and the factors are site (Site 1 and Site 2) and treatments (none, fertilizer, irrigation, fertilizer and irrigation).] What
3. Interaction When conducting two-way analysis of variance, if there is an interaction between the two factors, why should we not continue with separate tests for effects from the row and column factors?
2. Interaction What is an interaction, and what role does it play in two-way analysis of variance?
1. Two-Way ANOVA What is two-way analysis of variance, and what is it used for?
20. Using the Bonferroni Test Shown below are partial results from using the Bonferroni test with the sample data used in Exercise 14. Assume that a 0.05 significance level is being used.a. What do the displayed results tell us?b. Use the Bonferroni test procedure to find the significance value for
19. Using the Tukey Test This section included a display of the Bonferroni test results from Table 12-1. Shown here is the SPSS-generated display of results from the Tukey test. Compare the Tukey test results to those from the Bonferroni test.SPSS
18. Finding Components of ANOVA Exercise 9 is based on the weights of the 100 M&Ms listed in Data Set 13 in Appendix B. If the weights of all of the M&Ms from the full bag are used, SS(treatment) 5 0.00644, df(treatment) 5 5, SS(error) 5 1.47320, and df(error) 5 459.a. How many M&Ms are in the full
17. Equivalent Tests In this exercise you will verify that when you have two sets of sample data, the pooled t test for independent samples and the ANOVA method of this section are equivalent. Refer to the weights of the poplar trees in Table 12-1, but use only the data for the trees given no
16. Appendix B Data Set: Home Run Distances Refer to Data Set 17 in Appendix B.Use a 0.05 significance level to test the claim that the home runs hit by Barry Bonds, Mark McGwire, and Sammy Sosa have mean distances that are not all the same. Do the home run distances explain the fact that as of
15. Appendix B Data Set: Weights of Pennies Refer to Data Set 14 in Appendix B and use the weights of the Indian head pennies, wheat pennies, pre-1983 pennies, and post-1983 pennies. Use a 0.05 significance level to test the claim that the mean weight of pennies is the same for the four different
14. Archaeology: Skull Breadths from Different Epochs Samples of head breadths were obtained by measuring skulls of Egyptian males from three different epochs, and the measurements are listed below (based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver). Changes in head
13. Exercise and Stress A study was conducted to investigate the effects of exercise on stress. The table below lists systolic blood pressure readings (in mmHg) of subjects from the time preceding 25 minutes of aerobic bicycle exercise and preceding the introduction of stress through arithmetic and
12. Chest Deceleration in a Car Crash The chest deceleration data (g) are given below.Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?Subcompact: 55 47 59 49 42 Compact: 57 57 46 54 51
10. Solar Energy in Different Weather Astudent of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and analysis of variance was used with readings obtained on three different types of day: sunny,
9. Mean Weights of M&Ms Data Set 13 in Appendix B includes weights (in grams) of M&M plain candies categorized according to color (red, orange, yellow, brown, blue, and green). When STATDISK is used for analysis of variance with those data, the result is as shown below. Use a 0.05 significance
Fabric Flammability Tests in Different Laboratories Flammability tests were conducted on children’s sleepwear. The Vertical Semirestrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion was measured

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