Question

You wish to test the claim that the average IQ score is less than 100 at the .05 significance level. You determine the hypotheses are: H o : μ = 100 H 1 : μ < 100 You take a simple random sample of 38 individuals and find the mean IQ score is 98.8, with a standard deviation of 15.9. Let's consider testing this hypothesis two ways: once with assuming the population standard deviation is not known and once with assuming that it is known. Round to three decimal places where appropriate.

Assume Population Standard Deviation is NOT known

Assume Population Standard Deviation is 15

Test Statistic: t =

Test Statistic: z =

Critical Value: t =

Critical Value: z =

p-value:

Conclusion About the Null:

-Reject the null hypothesis

-Fail to reject the null hypothesis

Conclusion About the Null:

-Reject the null hypothesis

-Fail to reject the null hypothesis

Conclusion About the Claim:

-There is sufficient evidence to support the claim that the average IQ score is less than 100.

-There is NOT sufficient evidence to support the claim that the average IQ score is less than 100.

-There is sufficient evidence to warrant rejection of the claim that the average IQ score is less than 100.

-There is NOT sufficient evidence to warrant rejection of the claim that the average IQ score is less than 100.

Answer 1

Assume Population Standard Deviation is NOT known

Given:

= 100, n = 38, = 98.8, S = 15.9, = 0.05

Hypothesis:

Ho: = 100

Ha: < 100

Test statistic:

Critical value:

..................Using t table

P-value = 0.322 ...................Using t table

Conclusion:

Test statistic > Critical value, i.e. -0.465 > -1.687, That is Fail to Reject Ho at 5% level of significance.

ANSWER: B

B. Fail to reject the null hypothesis

ANSWER: B

B.  There is NOT sufficient evidence to support the claim that the average IQ score is less than 100

Assume Population Standard Deviation is known: = 15

Hypothesis:

Ho: = 100

Ha: < 100

Test statistic:

Critical value:

Z =Z_0.05 = -1.645 .....................Using Standard Normal Table

P-value = 0.311    .....................Using Standard Normal Table

Conclusion:

Test statistic > Critical value, i.e. -0.493 > -1.645, That is Fail to Reject Ho at 5% level of significance.

ANSWER: B

B. Fail to reject the null hypothesis

ANSWER: B

B.  There is NOT sufficient evidence to support the claim that the average IQ score is less than 100.