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1. A study of “adverse symptoms” in users of over-the-counter pain relief medications assigned subjects at random to one of two common pain relievers: acetaminophen and ibuprofen. In all, 650 subjects took acetaminophen, and 44 experienced some adverse symptom. Of the 347 subjects who took ibuprofen, 49 had an adverse symptom. We want to assess the evidence that the two pain relievers differ in the proportion of people who experience an adverse symptom. Construct and interpret a 90% confidence interval for the size of the difference. Choose an appropriate significance level, and perform a hypothesis test.

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2. In a study of heart surgery, one issue was the effect of drugs called beta-blockers on the pulse rate of patients during surgery. The available subjects were divided at random into two groups of 30 patients each. One group received a beta-blocker; the other group received a placebo. The pulse rate of each patient at a critical point during the operation was recorded. The treatment group had mean 65.2 and standard deviation For the control group, the mean was 70.3 and the standard deviation was 8.3. Give a 99% confidence interval for the difference in mean pulse rates. Interpret the confidence interval you obtain. Is there evidence that the mean pulse rate is different for the groups?

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3. In the 2001 regular baseball season, the World Series Champion Arizona Diamondbacks played 81 games at home and 81 games away. They won 48 of their home games and 44 of the games played away. We can consider these games as samples from potentially large populations of games played at home and away. Most people think that it is easier to win at home than away. Perform a significance test to determine whether this is true for the Arizona Diamondbacks.

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4. LeRoy, a starting player for a major college basketball team, made only 40% of his free throws last season. During the summer, he worked on developing a softer shot in hopes of improving his free throw accuracy. In the first eight games of this season, LeRoy made 25 free throws in 40 attempts. You want to investigate whether LeRoy’s work over the summer will result in a higher proportion of free throw successes this season.

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**5. “The nature of work is changing at whirlwind speed**

5. “The nature of work is changing at whirlwind speed. Perhaps now more than ever before, job stress poses a threat to the health of workers and, in turn, to the health of organizations.” So says the National Institute for Occupational Safety and Health. Employers are concerned about the effect of stress on their employees. Stress can lower morale and efficiency and increase medical costs. A large survey of restaurant employees found that 75% reported that work stress had a negative impact on their personal life. The human resources manager of a chain of restaurants is concerned that work stress may be affecting the chain’s employees. She asks a random sample of 100 employees to respond yes or no to the question, “Does work stress have a negative impact on your personal life?” Of these, 68 say “yes.” Is there evidence to conclude that the proportion for this chain of restaurants differs from the value given for the national survey? Use an appropriate inference procedure to support your answer.

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6. National Fuelsaver Corporation manufactures the Platinum Gasaver, a device they claim “may increase gas mileage by 22%.” Here are the percent changes in gas mileage for 15 identical vehicles, as presented in one of the company's advertisements: Conduct a hypothesis test to check the company’s claim.

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7. The Johns Hopkins Regional Talent Searches gives the Scholastic Aptitude Test (intended for high school juniors and seniors) to 13-year-olds. In all, 19,883 males and 19,937 females took the tests between 1980 and The mean scores of males and females on the verbal test are nearly equal, but there is a clear difference between the sexes on the mathematics test. The reason for this difference is not understood. Here are the summary data. Group mean s Males Females Determine if the male scores are significantly higher than the female scores at the a = 0.01 level.

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8. To help evaluate athletes coming out of college, the National Football League annually administers the Wunderlich test to all potential players. The test is used to measure a job candidate’s aptitude for learning and problem solving. Many players (through their agent) will prepare for the test, in order to earn a good score. One agent guarantees that his test prep method is effective, and compares a practice test he gives (the pre-test) to the actual test they are given by the NFL (the post-test) which follows intense test prep. Is their convincing evidence here that the test prep method of the agent is effective? WUNDERLICH SCORES: PreTest PostTest 17 21 8 13 25 24 31 33 19 16 12 11 6 8 19 23 35 36 22 23

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The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 8: Estimating with Confidence Section 8.2 Estimating a Population Proportion.

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