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Two proposed computer mouse designs were compared by recording wrist extension in degrees for 24 people who each used both mouse types ("Comparative Study of Two Computer Mouse Designs," Comell Human Factors Laboratory Technical Report RP7992). The difference in wrist extension was computed by subtracting extension for mouse type B from the wrist extension for mouse type A for each student. The mean difference was reported to be 8.82 degrees. Assume that it is reasonable to regard this sample of 24 people as representative of the population of computer users. a. Suppose that the standard deviation of the differences was 10 degrees. Is there convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B? Use 3 .05 significance level Dola For Borebe IL12 Position Paper Rider Fondominant Mendominant Player Combunt Arm Arm Pitcher Arm Arm 1057 31.3% 31.11 24.07 38 75 34.90 71.97 20.32 M6.70 24.71 26.15 21.10 28.87 21.19 25.51 17.30 3L19 20.47 21.DI 3600 21.75 31.58 12 17.92 12 32 55 17.85 13 21.56 25 2 14 15 20.20 21.50 15 24.54 27.15 13.77 17 12.59 IT 27.16 18 19 19 30 b. Suppose that the standard deviation of the differences was 26 degrees. Is there convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B? Use 3 .05 significance level c. Briefly explain why a different conclusion was reached in the hypothesis tests of Parts (a) and (b).\fSome people seem to believe that you can fix anything with duct tape. Even so, many were skeptical when researchers announced that duct tape may be a more effective and less painful alternative than liquid nitrogen, which doctors routinely use to freeze warts. The article "What a Fix-It; Duct Tape Can Remove Warts" (San Luis Obispo Tribune,October 15,2002] described a study conducted at Madigan Army Medical Center. Patients with warts were randomly assigned to either the duct tape treatment or the more traditional freezing treatment. Those in the duct tape group wore duct tape over the wart for 8 days, then removed the tape. soaked the area in water, and used an emery board to scrape the area. This process was repeated for a maximum of 2 months or until the wart was gone. Data consistent with values in the article are summarized in the following table: Treatment n Number with Wart Successfully Removed Liquid nitrogen freezing | 100 80 Duct tape 104 8.8 Do these data suggest that freezing is less successful than duct tape in removing warts? Test the relevant hypotheses using a significance level of .01. (Hint: See Example 11.9.)The authors of the paper "Adolescents and MP3 Players: Too Many Risks, Too Few Precautions" (Pediatrics [2009]: e953-e958) concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 784 Dutch boys and 748 Dutch girls age 12 to 19. Of the boys, 307 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting. Do the sample data support the authors' conclusion that the proportion of Dutch boys who listen to music at high volume is greater than this proportion for Dutch girls? Test the relevant hypotheses using a .01 significance level.After the 2010 earthquake in Haiti, many charitable organizations conducted fundraising campaigns to raise money for emergency relief. Some of these campaigns allowed people to donate by sending a text message using a cell phone to have the donated amount added to their cell-phone bill. The report "Early Signals on Mobile Philanthropy: Is Haiti the Tipping Point?" (Edge Research, 2010) describes the results of a national survey of 1526 people that investigated the ways in which people made donations to the Haiti relief effort. The report states that 17% of Gen Y respondents (those born between 1980 and 1980) and 14% of Gen X respondents (those born between 1908 and 1979) said that they had made a donation to the Haiti relief effort via text message. The percentage making a donation via text message was much lower for older respondents. The report did not say how many respondents were in the Gen Y and Gen X samples, but for purposes of this exercise, suppose that both sample sizes were 400 and that it is reasonable to regard the samples as representative of the Gen Y and Gen X populations. a. Is there convincing evidence that the proportion of those in Gen Y who donated to Haiti relief via text message is greater than the proportion for Gen X? Use o= .01. b. Estimate the difference between the proportion of Gen Y and the proportion of Gen X that made a donation via text message using a 09% confidence interval. Provide an interpretation of both the interval and the associated confidence level.The Insurance Institute for Highway Safety issued a press release titled "Teen Drivers Often Ignoring Bans on Using Cell Phones" (June 0, 2008). The following quote is from the press release: Just 1-2 months prior to the ban's Dec. 1. 2006 start, 11 percent of teen drivers were observed using cell phones as they left school in the afternoon. About 5 months after the ban took effect, 12% of teen drivers were observed using cell phones. Suppose that the two samples of teen drivers (before the ban, after the ban) can be regarded as representative of these populations of teen drivers. Suppose also that 200 teen drivers were observed before the ban (so n, = 200 and 1 5 .11) and 150 teen drivers were observed after the ban. a. Construct and interpret a 95% confidence interval for the difference in the proportion using a cell phone while driving before the ban and the proportion after the ban. b. Is zero included in the confidence interval of Part (c)? What does this imply about the difference in the population proportions?The press release referenced in the previous exercise also included data from independent surveys of teenage drivers and parents of teenage drivers. In response to a question asking if they approved of laws banning the use of cell phones and texting while driving. 74% of the teens surveyed and 95%% of the parents surveyed said they approved. The sample sizes were not given in the press release, but for purposes of this exercise, suppose that 800 teens and 400 parents of teens responded to the surveys and that it is reasonable to regard these samples as representative of the two populations. Do the data provide convincing evidence that the proportion of teens that approve of cell-phone and texting bans while driving is less than the proportion of parents of teens who approve? Test the relevant hypotheses using a significance level of .05.The article "Fish Oil Staves Off Schizophrenia" (USA Today, February 2. 2010) describes a study in which 81 patients age 13 to 25 who were considered atrisk for mental illness were randomly assigned to one of two groups. Those in one group took four fish oil capsules daily. The other group took a placebo. After 1 year, 5% of those in the fish oil group and 28% of those in the placebo group had become psychotic. Is it appropriate to use the two-sample z test of this section to test hypotheses about the difference in the proportions of patients receiving the fish oil and the placebo treatments who became psychotic? Explain why or why not.The report "Young People Living on the Edge" (Greenberg Quinlan Rosner Research, 2008) summarizes a survey of people in two independent random samples. One sample consisted of 800 young adults (age 19 to 35) and the other sample consisted of 300 parents of children age 19 to 35. The young adults were presented with a variety of situations (such as getting married or buying a house) and were asked if they thought that their parents were likely to provide financial support in that situation. The parents of young adults were presented with the same situations and asked if they would be likely to provide financial support to their child in that situation. a. When asked about getting married. 41% of the young adults said they thought parents would provide financial support and 43%% of the parents said they would provide support. Carry out a hypothesis test to determine if there is convincing evidence that the proportion of young adults who think parents would provide financial support and the proportion of parents who say they would provide support are different. b. The report stated that the proportion of young adults who thought parents would help with buying a house or apartment was .37. For the sample of parents, the proportion who said they would help with buying a house or an apartment was 27. Based on these data, can you conclude that the proportion of parents who say they would help with buying a house or an apartment is significantly less than the proportion of young adults who think that their parents would help?"Doctors Praise Device That Aids Ailing Hearts" (Associated Press, November 0, 2004) is the headline of an article that describes the results of a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. In the study, 107 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking- After two years, 38% of the 57 patients receiving the stocking had improved and 27% of the patients receiving the standard treatment had improved. Do these data provide convincing evidence that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment? Test the relevant hypotheses using a significance level of .05.The following quote is from the article "Canadians Are Healthier Than We Are" (Associated Press, May 31, 2006): "The Americans also reported more heart disease and major depression. but those differences were too small to be statistically significant." This statement was based on the responses of a sample of 5183 Americans and a sample of 3505 Canadians. The proportion of Canadians who reported major depression was given as .082. a. Assuming that the researchers used a one-sided test with a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .09? Explain why or why not. b. Assuming that the researchers used a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .10? Explain why or why not.Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments-mastectomy (removal of the breast) or lumpectomy (only the tumor is removed). In a long-term study of the effectiveness of these two treatments, 701 women with breast cancer were randomly assigned to one of two treatment groups. One group received mastectomies and the other group received lumpectomies and radiation. Both groups were followed for 20 years after surgery. It was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments (Associated Press, October 17, 2002). What hypotheses do you think the researchers tested in order to reach the given conclusion? Did the researchers reject or fail to reject the null hypothesis
