1. Assume the same data as are given in Problem 9. Suppose that the alternative hypothesis reads HA: X 85. Test the null hypothesis at the .05 significance level and state your conclusions.
2. The eighth-grade national norm for a social science test is a score of 123. The research director of a school district wants to know how the scores of pupils in his district compare with this standard. He selects a random sample of 81 students and finds that X 117. Assume X 10. (a) State the null hypothesis and alternative hypothesis best suited to the nature of his inquiry. Test the null hypothesis (b) at the .05 level of significance and state your conclusions and (c) at the .01 level of significance and state your conclusions.