Part III. Hypothesis Testing Based on a random sample of size 100 drawn from an arbitrary population, the analyst calculated the approximate symmetric 95% confidence interval for the population mean as (7.14, 11.06). 1. The analyst reported 9.1 as her point estimate of . Show that this number is consistent with the confidence interval she reported. (That is, show how it can be obtained from the C.I.) 2. Write down two justifications for using this value as the estimate of the unknown . 3. What is your estimate of the population variance 2 ? Defend your choice and give a numerical answer. 4. The analyst wrote: "The null hypothesis that the population mean equals 10 against the alternative that it is different from 10 cannot be rejected at the 5 percent level of significance." Do you agree? Defend your answer. 5. If you were to carry out the test described in 4 at the 10% level of significance, would you accept the null hypothesis? Explain briefly.