You may need to use the appropriate appendix table or technology to answer this question. Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (21 of which defaulted) and 80 loans approved by Norm (17 of which defaulted). (a) State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.) H0: Ha: (b) What is the sample default proportion for Carl? What is the sample default proportion for Norm? (c) Use a 0.05 level of significance. Calculate the test statistic. (Use p1 − p2. Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = What is your conclusion? Do not reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm. Do not reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm. Reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm. Reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.
You may need to use the appropriate appendix table or technology to answer this question.
Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (21 of which defaulted) and 80 loans approved by Norm (17 of which defaulted).
(a)
State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl's loans that default, and let p2 = the population proportion of Norm's loans that default. Enter != for ≠ as needed.)
H0:
Ha:
(b)
What is the sample default proportion for Carl?
What is the sample default proportion for Norm?
(c)
Use a 0.05 level of significance.
Calculate the test statistic. (Use
p1 − p2.
Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Do not reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.
Do not reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.
Reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.
Reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.
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