A school principal was interested in whether students in the chess club scored above or below the mean grade point average (GPA) at her school. She calculated the average GPA at the school to be 2.55 with σ = .5 and noted that the distribution was approximately normal. She then calculated the average GPA for 15 students in the chess club. Their mean GPA was 2.76. Did this group represent a population different from students in general at this school? (Use the .05 significance level.)

a) Use the four steps of hypothesis testing

b) Illustrate the distributions involved (Ho and H1 showing critical region)

c) Calculate the 95% confidence interval (*even if ns result)

* The four steps we learned was 

1. State the hypotheses and set the alpha level 

2. Locate the critical region 

3. Compute the test statistic for the sample 

4. Write a concluding statement about the null hypothessis based on the result of step 3.