Traditional method of hypothesis testing

A sample of ten local mixed martial arts studios shows their profits (in thousands of dollars) 5 years ago and their profits today. At ?=.05, can it be concluded that the average in profits for these studios is greater today than it was 5 years ago? Assume the variables are normally distributed. Use the traditional method of hypothesis testing. Hint: Make sure you think hard about your alternative hypothesis.

Studio ---- Profits 5 years ago ------ Profit Today

Dragon ---- 120 ------------------------------- 150

Monkey ---- 100 ------------------------------ 95

Phoenix ---- 200 ----------------------------- 260

Centaur ---- 80 ------------------------------- 100

Liger -------- 65 -------------------------------- 85

I've stated my hypotheses as H_{0}=113 and H_{1} > 113. I found the critical value as 1.65. But now I'm stuck on how to compute the test value.

Re: Traditional method of hypothesis testing

Hey Vold.

For this problem, your sample means have a distribution of N(mu,sigma^2/n) where n is the sample size, mu is the population mean and sigma^2 is the variance.

If you don't know the population variance, you can use the t-distribution which uses the sample variance and your test-statistic will belong to a t-distribution with n-1 degrees of freedom. Since your distributions are assumed to be normal, using this should be OK.

Also you may want to consider using H0: mu2 - mu1 < 0 vs H1: mu2 - mu1 > 0. Remember you are comparing two means; one from data five years ago and one from current data.