5) Any basketball fan knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off-season, Shaq had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level.    Check the conditions of the Central Limit Theorem for this scenario. Calculate the number of expected successes.

In a study of how depression may affect one's ability to survive a heart attack, the researchers reported the ages of the two groups they examined. The mean age of 2397 patients without cardiac disease was 69.8 years, while for the 450 patients with cardiac disease, the mean age was 74.0, respectively. Furthermore, 32% of the diseased group were smokers, compared with only 23.7% of those free of heart disease. (1) Determine a 96% confidence interval for the difference in the proportions of smokers in the two groups. (ii) Indicate whether the two groups in the study were different. State the assumptions in order to proceed with the confident interval construction. (ii)

Your statistics instructor often ponders the relationship between commute time and job satisfaction while driving back and forth to campus.  Your instructor hypothesizes that people with a shorter commute time will have higher degrees of job satisfaction.  Randomly sampling 600 Valley commuters, the instructor finds the following data listed in frequencies: Table 2: Commuters by Length of Commute and Job Satisfaction Job Satisfaction Number Who Commute 20 Minutes or Less Number Who Commute 21 to 40 Minutes Number Who Commute 41 Minutes or More Total Number for Each Level of Job Satisfaction Dissatisfied 10 60 140 210 Neutral 45 59 51 155 Satisfied 145 60 30 235 Total Number for Each Commute Time Range 200 179 221           1. Change frequencies to column percentages.

A health insurance company is looking at the use of its benefits by its members. It randomly selects 500 members for further study, and one of the pieces of information they collect is the amount the amount of money spent on prescription medications over the past year. The average amount among the 500 members is $600 and the SD is $1,000. A histogram of the amounts is quite skewed to the right, and 40 (8%) of the sampled members have spent $5000 or more on prescription medications in the past year. Calculate a 95%-confidence interval for the percentage of all members who have spent $5000 or more on prescription medications in the last year.