Suppose you have 30 observations from a normal distribution. The sample mean is 15 and the variance of X is 25. You want to test whether the sample mean is significantly different from 13.

a) Write down the null and alternative hypotheses

b) Calculate your Z statistic.

c) Can you reject the null hypothesis at the 5% significance level? (Report your critical value)

d) Can you reject the null hypothesis at the 1% significance level? (Report your critical value)

e) Report the 95% confidence interval for your sample.