The Internal Revenue Service is studying the category of charitable contributions. A sample of 34 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 34 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit. a. Explain why the hypergeometric distribution is appropriate. Because you are sampling a small population without replacement. O you are sampling a small population with replacement. O you are sampling a large population without replacement. b. What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) Probability c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) Probability

What is one indication that there are paired samples in a data set? Choose the correct answer below. O A. Knowing the value that a subject has in one group gives one no information about the value in the second group. OB. Each observation in one group is coupled with one particular observation in the other group. OC. The researcher is comparing two populations. O D. The researcher is working with two distinct groups in the data set.

The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1079 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample size Groups mean variance Less than h.s. High school Bachelor's 258 40.9 101.8 263 41.8 97.5 270 42.2 94.4 Graduate 288 43.0 98.7 Send data to calculator Send data to Excel To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the following statistic. Variation between the samples F= Variation within the samples For the data from…

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratiost. 9 20 11 35 19 13 15 21 29 53 16 26 21 14 21 27 10 12 47 14 40 18 60 72 33 14 8 49 5 16 8 19 12 31 67 51 26 18 17 20 19 13 25 23 27 44 20 27 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) (b) Find a 90% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper limit (c) Find a 99% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper…