Solved: Honesty Is the Best Policy In a USA Today survey

Problem 1BSC Smoking Cessation? The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a ?P?-value of 0.216 (rounded). What does the ?P?-value tell us about that claim? N N i N i c i c o c o t o t i t i n i n e n e I e P n G a h u t a m c l h e r S m o 1 2 9 k 9 6 5 i 1 3 n g N o t S m 5 5 2 o 9 7 7 k i n g

Problem 1CQQ Question? ?refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. D a y N u m b e r What are the null and alternative hypotheses corresponding to the stated claim?

Problem 1CRE Please be aware that some of the following problems may require knowledge of concepts presented in previous chapters. Weather-Related Deaths? Review Exercise 1 involved weather-related deaths. Among the 489 deaths included in the table, 325 are males. Use a 0.05 significance level to test the claim that among those who die in weather-related deaths, the percentage of males is equal to 50%. Exercise 1 ICU Patients? Listed below are the ages of randomly selected patients in intensive care units (based on data from “A Multifaceted Intervention for Quality Improvement in a Network of Intensive Care Units,” by Scales et al., ?Journal of the American Medical Association,? Vol. 305, No. 4). Find the mean, median, and standard deviation. Based on the results, is an age of 16 years ?unusual?.? Why or why not?

Problem 1RE Auto Fatalities? The table below lists auto fatalities by day of the week for a recent year (based on data from the Federal Highway Administration). Minitab results are also shown. Use a 0.01 significance level to test the claim that auto fatalities occur on the different days of the week with the same frequency. Can you provide an explanation for the results? D a y F r e q u e n c y

Problem 2BSC Terminology? The table in Exercise is called a contingency table or two-way table. Why is the term ?contingency? used? Why is the terminology of ?two-way table used? Exercise Smoking Cessation? The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a ?P?-value of 0.216 (rounded). What does the ?P?-value tell us about that claim? N N N i i i c c c o o o t t t i i i n n n e e e P I G a n t h u c a m h l e r S m o 1 2 9 k 9 6 5 i 1 3 n g N o t S m 5 5 2 o 9 7 7 k i n g

Problem 2CQQ Question? ?refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. D a y N u m b e r When testing the claim in Question, what are the observed and expected frequencies for Monday? Question What are the null and alternative hypotheses corresponding to the stated claim?

Problem 2CRE Cigarette Costs? In an American Express survey of 1000 adults 18 and older, 62% said that cigarettes should cost more to help offset potential negative health effects. Use the sample data to construct a 95% confidence interval estimate of the percentage of all adults who share that same belief. What can we conclude about a claim that half of all adults share that same belief?

Problem 2RE Measuring Weights? When certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more 0s or 5s. If we use the last digits (decimal portion) of the 80 weights in Data Set 1 from Appendix B, we get the frequency counts in the table below. Use a 0.05 significance level to test the claim that the last digits of 0, 1, 2, . . . , 9 occur with the same frequency. Does it appear that the weights were obtained through measurements? L a s t D i g i t F r e q u e n c y

Problem 3BSC Degrees of Freedom and Critical Value? For the hypothesis test in Exercise, the test statistic is 3.062. Find the number of degrees of freedom used to find the critical value, then find the critical value. Assume a 0.05 significance level. Exercise Smoking Cessation? The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a ?P?-value of 0.216 (rounded). What does the ?P?-value tell us about that claim? N N N i i i c c c o o o t t t i i i n n n e e e P I G a n t h u c a m h l e r S m o 1 2 9 k 9 6 5 i 1 3 n g N o t S m 5 5 2 o 9 7 7 k i n g

Problem 3CQQ Question? ?refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. D a y N u m b e r Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Problem 3CRE ICU Patients? Listed below are the ages of randomly selected patients in intensive care units (based on data from “A Multifaceted Intervention for Quality Improvement in a Network of Intensive Care Units,” by Scales et al., ?Journal of the American Medical Association,? Vol. 305, No. 4). Find the mean, median, and standard deviation. Based on the results, is an age of 16 years ?unusual?? Why or why not?

Problem 4BSC Right-Tailed, Left-Tailed, Two-Tailed? Is the hypothesis test in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice. Exercise Smoking Cessation? The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a ?P?-value of 0.216 (rounded). What does the ?P?-value tell us about that claim? N N N i i i c c c o o o t t t i i i n n n e e e G I P u n a m t h a c l h e r S m o 1 2 9 k 9 6 5 i 1 3 n g N o t S m 5 5 2 o 9 7 7 k i n g

Problem 4CQQ Question? ?refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. D a y N u m b e r If using a 0.05 significance level to test the stated claim, find the number of degrees of freedom and the critical value.

Problem 3RE Weather-Related Deaths? Listed below are the numbers of weather-related deaths in a recent year (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Can you provide an explanation for the result? M o n t h N u m b e r o f D e a t h s

Problem 4RE Bicycle Helmets? A study was conducted of 531 persons injured in bicycle crashes, and randomly selected sample results are summarized in the table shown on the next page (based on results from “A Case-Control Study of the Effectiveness of Bicycle Safety Helmets in Preventing Facial Injury,” by Thompson et al., ?American Journal of Public Health,? Vol. 80, No. 12). The TI-83/84 Plus calculator results also are shown. At the 0.05 significance level, test the claim that wearing a helmet has no effect on whether facial injuries are received. Based on these results, does a helmet seem to be effective in helping to prevent facial injuries in a crash? H e N l o m H e e t l W m o e r t n Facial 1 Injuries 3 8 Receive 0 2 d All 2 Injuries 8 3 Nonfaci 3 6 al

Problem 4CRE ICU Patients? Use the sample of ages from Exercise 1 to construct a 95% confidence interval estimate of the mean age of the population of ICU patients. Do the confidence interval limits contain the value of 65.0 years that was found from a sample of 9269 ICU patients? Exercise 1 ICU Patients? Listed below are the ages of randomly selected patients in intensive care units (based on data from “A Multifaceted Intervention for Quality Improvement in a Network of Intensive Care Units,” by Scales et al., ?Journal of the American Medical Association,? Vol. 305, No. 4). Find the mean, median, and standard deviation. Based on the results, is an age of 16 years ?unusual?? Why or why not?

Problem 5BSC In Exercise? est the given? ?claim. Denomination Effect? In a study of the “denomination effect” described in the Chapter Problem, 150 women in China were given either a single 100 Yuan bill or a total of 100 Yuan in smaller bills. The value of 100 Yuan is about $15. The women were given the choice of spending the money on specific items or they could keep the money. The results are summarized in the table below, and STATDISK results are provided in the screen display. Use a 0.05 significance level to test the claim that the form of the 100 Yuan is independent of whether the money was spent. What does the result suggest about a denomination effect? S K p e e p n t t t t h h e e M M o o n n e e y y Women Given a 6 1 Single 100-Yuan 0 5 Bill Women Given 100 6 Yuan in Smaller 7 8 Bills

Problem 5CQQ Question? ?refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. D a y N u m b e r Given that the ?P?-value for the hypothesis test is 0.971, what do you conclude?

Problem 5CRE Boats and Manatees? The table below lists the numbers of registered pleasure boats (thousands) in Florida and the numbers of watercraft-related manatee deaths for each year of the past decade. B o a t s M a n a t e e D e a t h s a. Test for a linear correlation between the numbers of boats and the numbers of manatee deaths. b. Find the equation of the regression line. Use the numbers of boats for the independent x? ?variable. c. What is the best predicted number of manatee deaths for the year preceding those included in the table? For that year, there were 84 (thousand) registered pleasure boats in Florida. How accurate is that predicted value, given that there were actually 78 manatee deaths in that year?

Problem 5RE Flipping and Spinning Pennies? Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in ?Chance News)?Does the conclusion change if the significance level is changed to 0.01? H e a Tails d s F l i 2 p 0 1992 p 4 i 8 n g S p i 9 n 5 1047 n 3 i n g

Problem 6CRE Forward Grip Reach and Ergonomics? When designing cars and aircraft, we must consider the forward grip reach of women. Women have normally distributed forward grip reaches with a mean of 686 mm and a standard deviation of 34 mm (based on anthropométrie survey data from Gordon, Churchill, et al.) a. If a car dashboard is positioned so that it can be reached by 95% of women, what is the shortest forward grip reach that can access the dashboard? b. If a car dashboard is positioned so that it can be reached by women with a grip reach greater than 650 mm, what percentage of women cannot reach the dashboard? Is that percentage too high? c. Find the probability that 16 randomly selected women have forward grip reaches with a mean greater than 680 mm. Does this result have any effect on the design?

Problem 6CQQ Question? ?refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. D I o O n n p F ’ p a t o v K s o n e r o w M 5 1 2 e 3 6 9 n 8 7 W 5 1 3 o 5 8 1 7 6 m e n Identify the null and alternative hypotheses corresponding to the stated claim.

Problem 6RE Home Field Advantage? Winning-team data were collected for teams in different sports, with the results given in the accompanying table (based on data from “Predicting Professional Sports Game Outcomes from Intermediate Game Scores,” by Copper, DeNeve, and Mosteller, ?Chance?, Vol. 5, No. 3–4). Use a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport. B a B F s a H o k s o o e e c t t b k b b a e a a l y l l l l l Ho 1 5 5 5 me 2 Tea 3 0 7 7 m Wi ns Vis itin g 7 4 4 4 Tea 1 7 3 2 m Wi ns

Problem 7BSC In Exercise?? est the given? ?claim. Testing a Lie Detector? The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truths and lies? Did the Subject Actuall y Lie? N Y o e ( s D ( i L d i N e o t d L ) i e ) Polygraph test indicated 1 4 that the subject lied 5 2 Polygraph test indicated 3 that the subject did not 9 2 lie

Problem 7CQQ refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. What distribution is used to test the stated claim (normal,?t, F,?chi-square, uniform)?

Problem 7CRE Honesty Is the Best Policy? In a ?USA Today? survey of 456 subjects, 269 agreed that honesty is always the best policy. Assume that we plan to use the survey results to estimate the proportion of the population who believe that honesty is always the best policy. a. Is the sample proportion of 269/456 a statistic or a parameter? b. Are frequency counts such as 269 categorical data or quantitative data? c. Are frequency counts such as 269 discrete or continuous? d. What does it mean for a sample, such as the 456 surveyed subjects, to be a simple random sample? e. The ?USA Today? survey was conducted as follows: A question was posted on the ?USA Today?Web site and Internet users could choose to respond. In statistics, is this a valid sampling plan?

Problem 8CQQ Question? ?refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. D I o O n n p F ’ p a t o v K s o n e r o w M 5 1 2 e 3 6 9 n 8 7 W 5 1 3 o 5 8 1 7 6 m e n Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Problem 8CRE Probability and Honesty? Based on the sample described in the preceding exercise, assume that when someone is randomly selected, there is a 0.6 probability that the selected person believes that honesty is always the best policy. a. If four people are randomly selected, find the probability that they all believe that honesty is always the best policy. b. If someone is randomly selected, what is the probability that he or she does ?not believe that honesty is always the best policy?

9CQQ Question refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. In Favor Oppose Don’t Know Men 538 167 29 Women 557 186 31 Find the number of degrees of freedom and the critical value.

9CQQ Question refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. In Favor Oppose Don’t Know Men 538 167 29 Women 557 186 31 Find the number of degrees of freedom and the critical value.

Problem 10BSC In Exercise, test the given claim. Nurse a Serial Killer? Alert nurses at the Veteran’s Affairs Medical Center in Northampton, Massachusetts, noticed an unusually high number of deaths at times when another nurse, Kristen Gilbert, was working. Those same nurses later noticed missing supplies of the drug epi-nephrine, which is a synthetic adrenaline that stimulates the heart. Kristen Gilbert was arrested and charged with four counts of murder and two counts of attempted murder. When seeking a grand jury indictment, prosecutors provided a key piece of evidence consisting of the table below. Use a 0.01 significance level to test the defense claim that deaths on shifts are independent of whether Gilbert was working. What does the result suggest about the guilt or innocence of Gilbert? Shifts with a Death Shifts without a Death Gilbert Was Working 40 217 Gilbert Was Not Working 34 1350

Problem 10CQQ Question refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. In Favor Oppose Don’t Know Men 538 167 29 Women 557 186 31 Given that the P-value for the hypothesis test is 0.836, what do you conclude?

Tennis Challenges The table below shows results since 2006 of challenged referee calls in the U.S. Open. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether the call is overturned.

Problem 12BSC In Exercise, test the given claim. Lefties A random sample of 760 subjects was obtained, and each was tested for left-hand writing. Results are in the table below (based on data from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519). Use a 0.05 significance level to test the claim that left-handedness is independent of gender. Writes with Left Hand? Yes No Male 23 217 Female 65 455

Problem 13BSC In Exercise, test the given claim. Soccer Strategy In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams (based on data from “Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks,” by Bar-Eli et al., Journal of Economic Psychology, Vol. 28, No. 5). In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks? Goalkeeper Jump Left Center Right Kick to Left 54 1 37 Kick to Center 41 10 31 Kick to Right 46 7 59

Is Seat Belt Use Independent of Cigarette Smoking? A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock, American Journal of Public Health, Vol. 67, No. 11). Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?

Problem 15BSC In Exercise, test the given claim. Clinical Trial of Echinacea In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). Use a 0.05 significance level to test the claim that getting a cold is independent of the treatment group. What do the results suggest about the effectiveness of echinacea as a prevention against colds? Treatment Group Placebo Echinacea: 20% extract Echinacea: 60% extract Got a Cold 88 48 42 Did Not Get a Cold 15 4 10

In Exercise, ?test the given? claim. Injuries and Motorcycle Helmet Color? A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the table below (based on data from “Motorcycle Rider Conspicuity and Crash Related Injury: Case-Control Study,” by Wells et al., BMJ USA, Vol. 4). Test the claim that injuries are independent of helmet color. Should motorcycle drivers choose helmets with a particular color? If so, which color appears best?

Problem 17BSC In Exercise, test the given claim. Survey Refusals A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below (based on data from “I Hear You Knocking But You Can’t Come In,” by Fitzgerald and Fuller, Sociological Methods and Research, Vol. 11, No. 1). At the 0.01 significance level, test the claim that the cooperation of the subject (response or refusal) is independent of the age category. Does any particular age group appear to be particularly uncooperative? Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 73 255 245 136 138 202 Refused 11 20 33 16 27 49

Problem 18BSC In Exercise, test the given claim. Baseball Player Births In his book Outliers, author Malcolm Gladwell argues that more American-born baseball players have birthdates in the months immediately following July 31 because that was the cutoff date for nonschool baseball leagues. The table below lists months of births for a sample of American-born baseball players and foreign-born baseball players. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America? Do the data appear to support Gladwell’s claim? Jan Feb March April May June July Aug Sept Oct Nov Dec Born in America 387 329 366 344 336 313 313 503 421 434 398 371 Foreign Born 101 82 85 82 94 83 59 91 70 100 103 82

Problem 19BSC Clinical Trial of Lipitor Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. (Until its patent expired in 2011, this was the largest-selling drug in the world, with annual sales of $13 billion.) Adverse reactions have been studied in clinical trials, and the table below summarizes results for infections in patients from different treatment groups (based on data from Parke-Davis). Use a 0.01 significance level to test the claim that getting an infection is independent of the treatment. Does the atorvastatin treatment appear to have an effect on infections? Placebo Atorvastatin 10 mg Atorvastatin 40 mg Atorvastatin 80 mg Infection 27 89 8 7 No Infection 243 774 71 87

Equivalent Tests A \(\chi 2\) test involving a \(2 \times 2\)table is equivalent to the test for the difference between two proportions, as described in Section 92. Using the claim and table in Example 4, verify that the \(\chi 2\) test statistic and the z test statistic (found from the test of equality of two proportions) are related as follows: \(z 2=\chi 2\) . Also show that the critical values have that same relationship. Equation Transcription: Text Transcription: \chi 2 2 \times 2 \chi 2 z 2=\chi 2

Problem 20BSC Genetics and Handedness In a study of left-handedness as a possible inherited trait, the data in the table below were obtained (based on data from “Why Are Some People Left-Handed? An Evolutionary Perspective,” by Laurens and Faurie, Philosophical Transactions,Vol. 364). Use a 0.01 significance level to test the claim that left-handedness is independent of parental handedness. What do the results suggest about the inheritability of left-handedness? Parental Handedness Offspring Left-Handed? Father/Mother Yes No Right/Right 5360 50,928 Right/Left 767 2736 Left/Right 741 3667 Left/Left 94 289

Using Yates's Correction for Continuity The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates's correction for continuity in cells with an expected frequency of less than 10 or in all cells of a contingency table with two rows and two columns. With Yates's correction, we replace \(\Sigma(O-E) 2 E \text { with } \Sigma(|O-E|-0.5) 2 E\) Given the contingency table in Example 4, find the value of the \(\chi 2\) test statistic using Yates's correction. What effect does Yates's correction have? Equation Transcription: Text Transcription: \Sigma(O-E) 2 E \text { with } \Sigma(|O-E|-0.5) 2 E \chi 2

Problem 1CQQ Question refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. Day Mon Tues Wed Thurs Fri Number 23 23 21 21 19 What are the null and alternative hypotheses corresponding to the stated claim?

Problem 1CRE Please be aware that some of the following problems may require knowledge of concepts presented in previous chapters. Weather-Related Deaths Review Exercise 1 involved weather-related deaths. Among the 489 deaths included in the table, 325 are males. Use a 0.05 significance level to test the claim that among those who die in weather-related deaths, the percentage of males is equal to 50%.

Auto Fatalities The table below lists auto fatalities by day of the week for a recent year (based on data from the Federal Highway Administration). Minitab results are also shown. Use a 0.01 significance level to test the claim that auto fatalities occur on the different days of the week with the same frequency. Can you provide an explanation for the results? MINITAB

Flipping and Spinning Pennies Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in Chance News.) Does the conclusion change if the significance level is changed to 0.01?

Problem 5RE Flipping and Spinning Pennies Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in Chance News)Does the conclusion change if the significance level is changed to 0.01? Heads Tails Flipping 2048 1992 Spinning 953 1047

Problem 6CQQ Question refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. In Favor Oppose Don’t Know Men 538 167 29 Women 557 186 31 Identify the null and alternative hypotheses corresponding to the stated claim.

Problem 4CQQ Question refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. Day Mon Tues Wed Thurs Fri Number 23 23 21 21 19 If using a 0.05 significance level to test the stated claim, find the number of degrees of freedom and the critical value.

Please be aware that some of the following problems may require knowledge of concepts presented in previous chapters. ICU Patients Use the sample of ages from Exercise 3 to construct a 95% confidence interval estimate of the mean age of the population of ICU patients. Do the confidence interval limits contain the value of 65.0 years that was found from a sample of 9269 ICU patients?

Bicycle Helmets A study was conducted of 531 persons injured in bicycle crashes, and randomly selected sample results are summarized in the accompanying table (based on results from “A Case­Control Study of the Effectiveness of Bicycle Safety Helmets in Preventing Facial Injury,” by Thompson et al., American Journal of Public Health, Vol. 80, No. 12). The TI­83/84 Plus calculator results also are shown. At the 0.05 significance level, test the claim that wearing a helmet has no effect on whether facial injuries are received. Based on these results, does a helmet seem to be effective in helping to prevent facial injuries in a crash?

Problem 1BSC Smoking Cessation The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a P-value of 0.216 (rounded). What does the P-value tell us about that claim? Nicotine Gum Nicotine Patch Nicotine Inhaler Smoking 191 263 95 Not Smoking 59 57 27

Problem 5CQQ Question refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. Day Mon Tues Wed Thurs Fri Number 23 23 21 21 19 Given that the P-value for the hypothesis test is 0.971, what do you conclude?

Problem 5CRE Boats and Manatees The table below lists the numbers of registered pleasure boats (thousands) in Florida and the numbers of watercraft-related manatee deaths for each year of the past decade. Boats 90 92 94 95 97 99 99 97 95 90 Manatee Deaths 81 95 73 69 79 92 73 90 97 83 a. Test for a linear correlation between the numbers of boats and the numbers of manatee deaths. ________________ b. Find the equation of the regression line. Use the numbers of boats for the independent xvariable. ________________ c. What is the best predicted number of manatee deaths for the year preceding those included in the table? For that year, there were 84 (thousand) registered pleasure boats in Florida. How accurate is that predicted value, given that there were actually 78 manatee deaths in that year?

Problem 2BSC Terminology The table in Exercise is called a contingency table or two-way table. Why is the term contingency used? Why is the terminology of two-way table used? Exercise Smoking Cessation The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a P-value of 0.216 (rounded). What does the P-value tell us about that claim? Nicotine Gum Nicotine Patch Nicotine Inhaler Smoking 191 263 95 Not Smoking 59 57 27

Problem 2CQQ Question refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. Day Mon Tues Wed Thurs Fri Number 23 23 21 21 19 When testing the claim in Question, what are the observed and expected frequencies for Monday? Question What are the null and alternative hypotheses corresponding to the stated claim?

Problem 2CRE Cigarette Costs In an American Express survey of 1000 adults 18 and older, 62% said that cigarettes should cost more to help offset potential negative health effects. Use the sample data to construct a 95% confidence interval estimate of the percentage of all adults who share that same belief. What can we conclude about a claim that half of all adults share that same belief?

Problem 6CRE Forward Grip Reach and Ergonomics When designing cars and aircraft, we must consider the forward grip reach of women. Women have normally distributed forward grip reaches with a mean of 686 mm and a standard deviation of 34 mm (based on anthropométrie survey data from Gordon, Churchill, et al.) a. If a car dashboard is positioned so that it can be reached by 95% of women, what is the shortest forward grip reach that can access the dashboard? ________________ b. If a car dashboard is positioned so that it can be reached by women with a grip reach greater than 650 mm, what percentage of women cannot reach the dashboard? Is that percentage too high? ________________ c. Find the probability that 16 randomly selected women have forward grip reaches with a mean greater than 680 mm. Does this result have any effect on the design?

Problem 6RE Home Field Advantage Winning-team data were collected for teams in different sports, with the results given in the accompanying table (based on data from “Predicting Professional Sports Game Outcomes from Intermediate Game Scores,” by Copper, DeNeve, and Mosteller, Chance, Vol. 5, No. 3–4). Use a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport. Basketball Baseball Hockey Football Home Team Wins 127 53 50 57 Visiting Team Wins 71 47 43 42

Problem 7BSC In Exercise, test the given claim. Testing a Lie Detector The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truths and lies? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Polygraph test indicated that the subject lied 15 42 Polygraph test indicated that the subject did not lie 32 9

ICU Patients Listed below are the ages of randomly selected patients in intensive care units (based on data from “A Multifaceted Intervention for Quality Improvement in a Network of Intensive Care Units,” by Scales et al., Journal of the American Medical Association, Vol. 305, No. 4). Find the mean, median, and standard deviation. Based on the results, is an age of 16 years unusual? Why or why not?

Problem 3RE Weather-Related Deaths Listed below are the numbers of weather-related deaths in a recent year (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Can you provide an explanation for the result? Month Jan Feb March April May June July Aug Sept Oct Nov Dec Number of Deaths 39 17 20 19 60 79 109 73 28 5 5 35

Problem 4BSC Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice. Exercise Smoking Cessation The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a P-value of 0.216 (rounded). What does the P-value tell us about that claim? Nicotine Gum Nicotine Patch Nicotine Inhaler Smoking 191 263 95 Not Smoking 59 57 27

Problem 8CQQ Question refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. In Favor Oppose Don’t Know Men 538 167 29 Women 557 186 31 Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Problem 8CRE Probability and Honesty Based on the sample described in the preceding exercise, assume that when someone is randomly selected, there is a 0.6 probability that the selected person believes that honesty is always the best policy. a. If four people are randomly selected, find the probability that they all believe that honesty is always the best policy. ________________ b. If someone is randomly selected, what is the probability that he or she does not believe that honesty is always the best policy?

Measuring Weights When certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more 0s or 5s. If we use the last digits (decimal portion) of the 80 weights in Data Set 1 from Appendix B, we get the frequency counts in the table below. Use a 0.05 significance level to test the claim that the last digits of 0, 1, 2,..., 9 occur with the same frequency. Does it appear that the weights were obtained through measurements?

Problem 3BSC Degrees of Freedom and Critical Value For the hypothesis test in Exercise, the test statistic is 3.062. Find the number of degrees of freedom used to find the critical value, then find the critical value. Assume a 0.05 significance level. Exercise Smoking Cessation The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and Prevention. If we test the claim that success is independent of the method used, the TI-83/84 Plus calculator provides a P-value of 0.216 (rounded). What does the P-value tell us about that claim? Nicotine Gum Nicotine Patch Nicotine Inhaler Smoking 191 263 95 Not Smoking 59 57 27

Problem 3CQQ Question refer to the sample data in the following table (based on data from the Bureau of Labor Statistics). The table lists frequencies for randomly selected nonfatal occupation injuries arranged according to day of the week. Assume that we want to use a 0.05 significance level to test the claim that such injuries occur with equal frequency on different days of the week. Day Mon Tues Wed Thurs Fri Number 23 23 21 21 19 Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Questions 6–10 refer to the sample data in the following table (based on data from the Pew Research Center). Randomly selected subjects were asked about the use of marijuana for medical purposes. Assume that we want to use a 0.05 significance level to test the claim that response to the question is independent of gender. What distribution is used to test the stated claim (normal, t, F, chi­-square, uniform)?

Problem 7CRE Honesty Is the Best Policy In a USA Today survey of 456 subjects, 269 agreed that honesty is always the best policy. Assume that we plan to use the survey results to estimate the proportion of the population who believe that honesty is always the best policy. a. Is the sample proportion of 269/456 a statistic or a parameter? ________________ b. Are frequency counts such as 269 categorical data or quantitative data? ________________ c. Are frequency counts such as 269 discrete or continuous? ________________ d. What does it mean for a sample, such as the 456 surveyed subjects, to be a simple random sample? ________________ e. The USA Today survey was conducted as follows: A question was posted on the USA TodayWeb site and Internet users could choose to respond. In statistics, is this a valid sampling plan?

Problem 8BSC In Exercise, test the given claim. Discrimination The U.S. Supreme Court considered a case involving the exam for firefighter lieutenant in the city of New Haven, Connecticut. Results from the exam are shown in the table below. Is there sufficient evidence to support the claim that results from the test should be thrown out because they are discriminatory? Use a 0.01 significance level. Passed Failed White Candidates 17 16 Minority Candidates 9 25