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Which method? Which of the following scenarios should be analyzed as paired data? a. Students take an MCAT prep course. Their before and after scores are compared. b. 20 male and 20 female students in class take a midterm. We compare their scores. c. A group of college freshmen are asked about the quality of the university cafeteria. A year later, the same students are asked about the cafeteria again. Do student's opinions change during their time at school?

Which method II? Which of the following scenarios should be analyzed as paired data? a. Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives. b. 50 insomnia patients are given a placebo and 50 are given a mild sedative. Which subjects sleep more hours? c. A group of college freshmen and a group of sophomores are asked about the quality of the university cafeteria. Do students' opinions change during their time at school?

Music Some students do homework with music playing in their headphones. (Anyone come to mind?) Some researchers want to see if people can work as effectively with as without distraction. The researchers will time some volunteers to see how long it takes them to complete some relatively easy crossword puzzles. During some of the trials, the room will be quiet; during other trials in the same room, subjects will wear headphones and listen to a Pandora channel. a. Design an experiment that will require a two-sample \(t-\) procedure to analyze the results. b. Design an experiment that will require a matched-pairs \(t-\) procedure to analyze the results. c. Which experiment would you consider the stronger design? Why?

Freshman 15 ? Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true. a. Describe a study design that would require a matched-pairs t-procedure to analyze the results. b. Describe a study design that would require a two-sample \(t-\) procedure to analyze the results.

Women Values for the labor force participation rate of women (LFPR) are published by the U.S. Bureau of Labor Statistics. We are interested in whether there was a difference between female participation in 1968 and \(1972,\) a time of rapid change for women. We check LFPR values for 19 randomly selected cities for 1968 and \(1972 .\) Shown below is software output for two possible tests: Paired \(t\) -Test of \(\mu(1-2)\) Test \(\mathrm{H}_{0}: \mu(1972-1968)=0\) vs ??: \(\mu(1972-1968) \neq 0\) Mean of Paired Differences \(=0.0337\) \(t\) -Statistic \(=2.458\) with \(18 \mathrm{df}\) \(p=0.0244\) 2-Sample \(t\) -Test of \(\mu 1-\mu 2\) Ho : \(\mu 1-\mu 2=0\) Ha: \(\mu 1-\mu 2 \neq 0\) Test \(\mathrm{Ho}: \mu(1972)-\mu(1968) \neq 0 \mathrm{vs}\) \(\mathrm{Ha}: \mu(1972)-\mu(1968) \neq 0\) Difference Between Means \(=0.0337\) \(t\) -Statistic \(=1.496\) with \(35 \mathrm{df}\) \(p=0.1434\) a. Which of these tests is appropriate for these data? Explain. b. Using the test you selected, state your conclusion.

Friday the 13 th, traffic The British Medical Journal (1993; \(307: 1584)\) published an article titled, "Is Friday the 13 th Bad for Your Health?" Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13 th. The data below are the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6 th and 13 th ) for five different periods. Here are summaries of two possible analyses: Paired \(t\) -Test; Mean of Paired Differences: 1835.8 \(t\) -Statistic \(=4.936\) with \(9 \mathrm{df}\) \(\mathrm{P}=0.0008\) 2-Sample \(t\) -Test Difference Between Means: 1835.8 \(t\) -Statistic \(=0.5499\) with 17 df \(\mathrm{P}=0.5891\) a. Which of the tests is appropriate for these data? Explain. b. Using the test you selected, state your conclusion. c. Are the assumptions and conditions for inference met?

Friday the 13 th, accidents The researchers in Exercise 15 ?also examined the number of people admitted to emergency rooms for vehicular accidents on 12 Friday evenings \((6\) each on the 6 th and 13 th ). Based on these data, is there evidence that more people are admitted, on average, on Friday the 13 th? Here are two possible analyses of the data: Paired \(t\) -Test of \(\mu(1-2)=0\) vs. \(\mu(1-2)<0\) Mean of Paired Differences \(=-3.333\) \(t\) -Statistic \(=-2.7116\) with \(5 \mathrm{df}\) \(\mathrm{P}=0.0211\) 2-Sample \(t\) -Test of \(\mu 1=\mu 2\) vs. \(\mu 1<\mu 2\) Difference Between Means \(=-3.333\) \(t\) -Statistic \(=-1.6644\) with \(9.940 \mathrm{df}\) \(\mathrm{P}=0.0636\) a. Which of these tests is appropriate for these data? Explain. b. Using the test you selected, state your conclusion. c. Are the assumptions and conditions for inference met?

Wind speed, part I To select the site for an electricitygenerating wind turbine, wind speeds were recorded at several potential sites every 6 hours for a year. Two sites not far from each other looked good. Each had a mean wind speed high enough to qualify, but we should choose the site with a higher average daily wind speed. Because the sites are near each other and the wind speeds were recorded at the same times, we should view the speeds as paired. Here are the summaries of the speeds (in miles per hour): Is there a mistake in this output? Why doesn't the Pythagorean Theorem of Statistics (see p. 620 ) work here? In other words, shouldn't $$ S D(\text { site } 2-\text { site4 })=\sqrt{S D^{2}(\text { site } 2)+S D^{2}(\text { site4 }) ?} $$ But \(\sqrt{(3.586)^{2}+(3.421)^{2}}=4.956,\) not 2.551 as given by the software. Explain why this happened.

BST Many dairy cows now receive injections of BST, a hormone intended to spur greater milk production. After the first injection, a test herd of 60 Ayrshire cows increased their mean daily production from 47 pounds to 61 pounds of milk. The standard deviation of the increases was 5.2 pounds. We want to estimate the mean increase a farmer could expect in his own cows. a. Check the assumptions and conditions for inference. b. Write a \(95 \%\) confidence interval. c. Explain what your interval means in this context. d. Given the cost of BST, a farmer believes he cannot afford to use it unless he is sure of attaining at least a \(25 \%\) increase in milk production. Based on your confidence interval, what advice would you give him?