Question

Please Help! Need to confirm my answer.

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:

Ho: μ = 100
H1: μ < 100

You take a simple random sample of 100 individuals and find the mean IQ score is 95.7, with a standard deviation of 16. 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: (Pick One) Reject the null hypothesis Fail to reject the null hypothesis	Conclusion About the Null: (Pick One) Reject the null hypothesis Fail to reject the null hypothesis
Conclusion About the Claim: (Pick One) 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: (Pick One) 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

sample std dev ,    s =    16.0000
Sample Size ,   n =    100
Sample Mean,    x̅ =   95.7000

Assume Population Standard Deviation is NOT known	Assume Population Standard Deviation is 15
Test Statistic: t =(x̅ - µ )/(s/√n) = -2.6875	Test Statistic: z =(x̅ - µ )/(σ/√n) = -2.8667
DF=n-1=   99 Critical Value: t = -2.3646	Critical Value: z = - 2.3263
p-value:=0.0042	p-value:= 0.0021
Conclusion About the Null: p value <α,so Reject the null hypothesis	Conclusion About the Null:p value <α,so Reject the null hypothesis
Conclusion About the Claim: (Pick One) There is sufficient evidence to support the claim that the average IQ score is less than 100.	Conclusion About the Claim: (Pick One) There is sufficient evidence to support the claim that the average IQ score is less than 100.