Question

You wish to test the claim that the average IQ score is less than 100 at the .01 significance level. You determine the hypotheses are: H o : μ = 100 H 1 : μ < 100 You take a simple random sample of 60 individuals and find the mean IQ score is 98.7, with a standard deviation of 14.6. 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: 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. 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. Is there a significant difference between when we know the population standard deviation and when we don't? Explain.

Answer 1

from above:

Test Statistic: t = -0.690

Test Statistic: z = -0.690

Critical Value: t = -2.391

Critical Value: z = -2.326 ~ -2.33

p-value for t test statistic =0.2465

p-value for z test statistic =0.2451

Fail to reject the null hypothesis

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