6) The grade point averages for 10 randomly selected junior college students are listed below. Assume the grade point averages are normally distributed. Find a 98% confidence interval for the true mean. Round to the nearest hundredth. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 7) The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that =14 minutes based on previous studies. 8) The business college computing center wants to determine the proportion of business students who have personal computers (PCs) at home. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have PCs at home. Find the rejection region for this test using =0.10. 9) A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of 100 doctors results in 83 who indicate that they recommend brand Z. Determine the test statistic for this problem (round to the nearest hundredth). 10) Fifty percent of registered voters in a congressional district are registered, Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Democratic candidate. Does the Republican candidate have a chance to win? Use =0.05.