Question

The designer of a 100-point aptitude test wishes test scores to have a standard deviation of 10. He gives the test to 25 randomly selected college students in order to test the null-hypothesis σ²=100 against the alternative hypothesis σ² ≠ 100 at the level α= .02. Suppose he found s²= 70. Perform an appropriate hypothesis test.

Answer 1

Null hypothesis :H_o :   =100

Alternate hypothesis : H_a : 100

Given
Hypothesized Variance : = 100	10
Sample Variance: s2	70
Sample Size : n	25
Level of significance :	0.02
Degrees of Freedom : n-1	24

For 24 degrees of freedom :

Critical values : For 24 degrees of freedom

For Two tailed test;

Fail to reject null hypothesis if Value of the test statistic is within critical values : and   .

As Value of the test statistic is with in the Critical Values i.e.( 10.8564 < 16.8 < 42.9798 )Fail To Reject Null Hypothesis

Not enough evidence to conclude that the variance is not 100 (or the standard deviation is not 10)