9. From a normal distribution with a mean of 40 and a standard deviation of 10, a random sample of 64 was drawn. The mean of this sample was 48. An investigator thinks that the mean of the sample is different than the population mean.

a. What is the null hypothesis for a two-tailed test? What is the alternative hypothesis?

b. What is the appropriate test statistics we should use to answer part a?

c. For the two-tailed hypothesis, calculate the appropriate statistics and decide whether or not to reject the null hypothesis at the .05 level.

d. Calculate the 90% CI, the 95% CI, and the 99% CI.