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 your sample is significantly greater than 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)