5) According to a basketball coach, the mean height of all female college basketball players is 69.5 inches. A random sample of 25 such players produced a mean height of 71.2 inches with a standard deviation of 2.4 inches. Assuming that the heights of all female college basketball players are normally distributed, test the coach's claim at a 5% level of significance. 6) A mail order company claims that at least 70% of all orders are mailed within 48 hours. From time to time the quality control department checks to see if this promise is fulfilled. Recently the quality control department at this company took a sample of 400 orders and found that 244 of them were mailed within 48 hours. Testing at the 0.5% significance level, can you conclude that the company's claim is true? 7) A teacher claims that his grades are distributed as follows: 14% are an A, 20% are a B, 30% are a C, 20% are a D, and the rest are an F. A recent survey of his classes shows 25 students got an A, 48 got a B, 63 got a C, 43 got a D, and 31 got an F. Using a 5% level of significance test whether the teacher's claim is supported by the survey. 8) In a recent study, students were asked if they formed study groups to prepare for tests. Each student in the study was classified according to academic performance at school and was asked if they had regularly participated in a study group. The results obtained from the survey are summarized in the table. Using a 5% level of significance, can you conclude that school performance and participation in study groups? Group Study Yes No School Excellent 38 38 Performance Average 27 45 Below 13 28 Average 9) A survey was conducted to see if people have a preference for television shows. They are asked if they prefer sports, news, reality shows, dramas, or comedies. The results were that 22 people preferred sports, 14 preferred news, 26 preferred reality shows, 20 preferred dramas, and 28 preferred comedies. Conduct a test for goodness of fit at a 10% level of significance.