Question

) Scores on an IQ test are normally distributed. A sample of 20 IQ scores had standard deviation s = 8. The developer of the test claims that the population standard deviation is ı = 12. Do these data provide sufficient evidence to contradict this claim? Use the Į = 0.05 level of significance.
3)
A) Reject H0. The population standard deviation appears to differ from 12. B) Do not reject H0. There is insufficient evidence to conclude that the population standard deviation differs from 12.

Answer 1

Solution:

Given:

Sample Size = n = 20

Sample Standard deviation = s = 8

Claim: Population standard deviation =

Level of significance =

We have to test if these data provide sufficient evidence to contradict this claim.

Step 1) State H0 and H1:

Since claim is non-directional , this is two tailed test.

Vs

Step 2) Test statistic:

Step 3) Chi-square critical values:

df = n - 1 = 20 - 1 = 19

Level of significance =

Since this is two tailed test, find

and

Thus Chi-square critical values are: ( 8.907 , 32.852 )

Step 4) Decision Rule:

Reject null hypothesis H0,
if Chi square test statistic < Chi-square critical value =8.907 or Chi square test statistic > Chi-square critical value=32.852, otherwise we fail to reject H0.

Since  Chi square test statistic < Chi-square critical value =8.907, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance,  these data provide sufficient evidence to contradict this claim.

That is: The population standard deviation appears to differ from 12.

Thus correct answer is:

A) Reject H0. The population standard deviation appears to differ from 12.