The student population at the state college consists of 60% females and 40% males. A.  The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 37 females and 18 males. Is the gender distribution for theatergoers significantly different from the distribution for the general college? Test at the .05 level of significance. B. The same researcher also recorded the gender of each student watching a men’s basketball game in the college gym and found a total of 58 females and 82 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the .05 level of significance.

Bank of America's Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2) Using the difference data, the sample mean difference was d = $850, and the sample standard deviation was så = $1,123. a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. Ho : μα ♦ Select your answer - Ha d + - Select your answer - b. Use a = = 0.05 level of significance. Can you conclude that the population means differ? - Select your answer - ◆ What is the p-value? (to 6 decimals) c.…

2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.      Age Group     Watch11 p.m. News? 18 or less 19 to 35 36 to 54 55 or Older Total Yes 49 59 61 84 253 No 201 191 189 166 747 Total 250 250 250 250 1,000     (a) Let p1, p2, p3, and p4 be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H0 that p1, p2, p3, and p4 are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)…