Suppose that you want to convince your friends that the male freshmen are taller than the seniors. To answer this question, you have sampled 41 freshman boys as well as 41 senior boys. The average height of the 41 freshmen is 178cm and the average height of the 41 seniors is 175cm. Further the variance of the freshman group is 100 and 144 for the senior group. Suppose the same population standard deviation of the two groups.
a. Develop the null and alternative hypothesis.
b. What distribution do we use to implement the hypothesis testing?
c. With a significance level of 0.05, should you reject the null hypothesis?