Question

In 2004, the standard deviation of the math scores of the students at Stanford was 50. Recently, a sample of 20 students had a standard deviation of 45. We are interested in testing to see if there has been a significant change in the standard deviation of math scores at Standford.

a. Develop null hypotheses and alternative hypotheses.

b. What is the value of test statistic?

c. At 95% confidence, what is the critical values?

Answer 1

Part a

Null hypothesis: H0: the standard deviation of the math scores of the students at Stanford is 50.

Alternative hypothesis: Ha: the standard deviation of the math scores of the students at Stanford is not 50.

Part b

Test statistic = Chi-square = (n – 1)*S^2/σ^2

Chi-square = (20 - 1)*45^2/50^2 = 15.39

Test statistic = 15.39

Part c

Confidence level = 95% = 0.95

α = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

So, critical values by using Chi-square table are given as below:

Critical values: 8.9065 and 32.8523