It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage.   a) If he wants to limit the margin of error of his 95% confidence interval to 1%, what is the minimum amount of money he needs to set aside to pay his subjects?

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 ​respondents, 14​% chose chocolate​ pie, and the margin of error was given as ±5 percentage points. Describe what is meant by the statement that​ "the margin of error was given as ±5 percentage​ points." Choose the correct answer below.     A. The statement indicates that the study is only 5​% confident that the true population percentage of people that prefer chocolate pie is exactly 14​%.   B. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 14​%±5​%.   C. The statement indicates that the interval 14​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework.     We want to test ?0:?=0.75;??:?<0.75H0:p=0.75;Ha:p<0.75, where ?p = the true proportion of the students at Mr. Tabor’s school who completed their math homework last night. A significance test yields a ?P-value of 0.1265. What it would mean for the null hypothesis to be true in this setting? 1. Mr. Tabor’s students complete 75% of their homework last night. 2.cIf ?0:?=0.75H0:p=0.75 is true, then the proportion of the homework that the students at Mr. Tabor’s school completed last night is 0.75. 3. If ?0:?=0.75H0:p=0.75 is true, then the proportion of the sample who completed their homework last night is 0.75. 4. If ?0:?=0.75H0:p=0.75 is true, then the proportion of all students at Mr.…

Smallpox Vaccine.ABCNEWS.com published the results of a poll that asked U.S. adults whether they would get a smallpox shot if it were available. Sampling, data collection, and tabulation were done by TNS Intersearch of Horsham, Pennsylvania. When the risk of the vaccine was described in detail, 4 in 10 of those surveyed said they would take the smallpox shot. According to the article, “the results have a three-point margin of error” (for a 0.95 confidence level). Use the information provided to obtain a 95% confidence interval for the percentage of all U.S. adults who would take a smallpox shot, knowing the risk of the vaccine.

A report on electronic monitoring and surveillance summarized a survey of 308 U.S. businesses. The report stated that 91 of the 308 businesses had fired workers for misuse of the Internet. Assume that this sample is representative of businesses in the United States.   Use the sample data to estimate the standard error of p̂. (Round your answer to three decimal places.)     Calculate the margin of error associated with the estimate in part (a). (Round your answer to three decimal places.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increasefor company 24 25 27 18 6 4 21 37 A: Percent increasefor CEO 21 23 24 14 −4 19 15 30 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Let d = B − A.) What is…

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increasefor company 24 25 25 18 6 4 21 37 A: Percent increasefor CEO 21 25 22 14 −4 19 15 30   Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Let d = B − A.)…

A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 11% chose chocolate pie, and the margin of error was given as ±3 percentage points. Describe what is meant by the statement that "the margin of error was given as ±3 percentage points." Choose the correct answer below. A. The statement indicates that the study is 100% - 3% = 97% confident that the true population percentage of people that prefer chocolate pie is 11%. B. The statement indicates that the interval 11% ± 3% is likely to contain the true population percentage of people that prefer chocolate pie. C. The statement indicates that the study is only 3% confident that the true population percentage of people that prefer chocolate pie is exactly 11%. D. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11% ± 3%.

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t-table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below. Location of Wolf Pack % Males (Winter) % Males (Summer) Finland 60 42 Finland 51 56 Finland 87 71 Lapland 55 48 Lapland 64 55 Russia 50 50 Russia 41 50 Russia 55 45   What is the value of the sample test statistic? (Round your answer to three decimal places.)