Question

2. 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

   c) Calculate the 95% confidence interval {*even if ns (non-significant result)}

Answer 1

Given : Sample size=n=15

Sample mean=

Population standard deviation=

Population mean=

Significance level=

a) Hypothesis : Vs  

The test statistic is ,

Critical value :

Rejection Region :

Decision : Here ,

Therefore , fail to reject the Ho

Conclusion : Hence , there is not sufficient evidence to conclude that the students in the chess club scored above or below the mean grade point average (GPA) at her school.

(b) Here , population standard deviation is known

Therefore , use the normal distribution

(c) The 95% confidence interval is ,