Need a little help. Please help
You wish to test the claim that the average IQ score is less than 100 at the .10 significance level. You determine the hypotheses are:
Ho : μ = 100 H 1 : μ < 100
You take a simple random sample of 41 individuals and find the mean IQ score is 97.2, with a standard deviation of 14.9. 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: | p-value: |
Conclusion About the Null: (pick one)
|
Conclusion About the Null: (pick one)
|
Conclusion About the Claim: (pick one)
|
Conclusion About the Claim: (pick one)
|
Is there a significant difference between when we know the population standard deviation and when we don't? Explain.
Assume Population Standard Deviation is NOT known |
Sample size = n = 41
Sample mean = = 97.2
Standard deviation = s = 14.9
Here population standard deviation is unknown so we have to use
t-test statistic.
Test statistic is
Degrees of freedom = n - 1 = 41 - 1 = 40
Level of signficance = 0.10
Critical value = 1.303
P-value = P(T < - 1.20) = 0.1180
P-value > 0.10 we fail to reject null hypothesis.
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Assume Population Standard Deviation is 15
Sample size = n = 41
Sample mean = = 97.2
Population standard deviation = = 15
Here population standard deviation is known so we have to use z-test statistic.
Test statistic is
Critical value = 1.28
P-value = P(Z < - 1.20) = 0.1160
P-value > 0.10 we fail to reject null hypothesis.
Need a little help. Please help You wish to test the claim that the average IQ...
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