Question

Suppose that a sample has been drawn from a normal population to conduct the hypothesis test

H0:σ2=33

H1:σ2>33

Assume that you know that the sample variance is s2=63, the sample size is n=24, and take α=0.09. Draw the sampling distribution, and use it to determine each of the following:

A. The test statistic is:

B. The p-value is

C. Your decision for the hypothesis test:

A. Do Not Reject H1H1.
B. Do Not Reject H0H0.
C. Reject H0H0.
D. Reject H1H1.

Answer 1

Given that, sample size (n) = 24 and

sample variance (s​​​​​​2) = 63

The null and alternative hypotheses are,

A) Test statistic is,

=> Test statistic = 43.909

B) Using Excel we find, the p-value

Degrees of freedom = 24 - 1 = 23

Excel Command : =CHIDIST(43.909, 23) = 0.0054

p-value = 0.0054

c) Since, p-value is less than α=0.09, we reject the null hypothesis.

Therefore, your decision for the hypothesis test : Reject H0