Question

You wish to test the claim that the average IQ score is less than 100 at the .005 significance level. You determine the hypotheses are: Ho:u= 100 H1:4 < 100 You take a simple random sample of 72 individuals and find the mean IQ score is 96.7, with a standard deviation of 15.5. 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 Test Statistic: t = Critical Value: t = p-value: Conclusion About the Null: Assume Population Standard Deviation is 15 Test Statistic: z = Critical Value: z = p-value: Conclusion About the Null: Reject the null hypothesis Fail to reject the null hypothesis Reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Claim: Conclusion About the Claim: There is sufficient evidence to support the claim that the average IQ score is less than 100. 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 NOT sufficient evidence to support the claim that the average IQ score is less than 100.
PLEASE HELP ME OUT WITH BOTH QUESTIONS!!!

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Answer 1

Solution:

You wish to test the claim that the average IQ score is less than 100 at the .005 significance level. You determine the hypotheses are: Ho: u= 100 H:p100 You take a simple random sample of 72 individuals and find the mean IQ score is 96.7, with a standard deviation of 15.5. 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 Test Statistic: t= -1.807 Assume Population Standard Deviation is 15 Test Statistic: z= -1.867 Critical Value: t Critical Value: z = -2.647 -2.576 p-value: 0.038 p-value: 0.031 Conclusion About the Null: Conclusion About the Null: Reject the null hypothesis Reject the null hypothesis Fail to reject the null hypothesis Fail to reject the null hypothesis Conclusion About the Claim: Conclusion About the Claim: There is sufficient evidence to support the claim that the average There is sufficient evidence to support the claim that the averrage IQ score is less than 100 iQ score is less than 100. There is NOT sufficient evidence to support the claim that the There is NOT sufficient evidence to support the claim that the average IQ score is less than 100, average IQ score is less than 100 CThere is sufficient evidence to warrant rejection of 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 There is NOT sufficient evidence to warrant rejection of the claim that the average IQ score is less than 100 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. Edit Insert FormatsBI Ų x xAA No, there is not a significant difference between when we know the population standard and when we don't because the population standard deviation and sample standard deviation are very close

This year, a company wishes to use their employment drug screening to test a claim. They take a simple random sample of 2441 job applicants and find that 114 individuals fail the drug test for cocaine. They want to test the claim that the proportion of the population failing the test is lower than 5.6%. Use .10 for the significance level. Round to three decimal places where appropriate. Hypotheses H:p 5.6% H p5.6% Test Statistic:z -1.998 Critical Value: z =-1.282 p-value: 0.023 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 proportion of the population failing the test is lower than 5.6% CThere is NOT sufficient evidence to support the claim that the proportion of the population failing the test is lower than 5.6% CThere is sufficient evidence to warrant rejection of the claim that the proportion of the population failing the test is lower than 5.6% There ic NOT ffirient evidence to warrant reiertion of the claim that the nronortion of the nonulation failing the tact ie Inwor than 5 60%