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Hypothesis testing and interval estimation 6. Hypothesis testing and interval es

ID: 3151660 • Letter: H

Question

Hypothesis testing and interval estimation

6. Hypothesis testing and interval estimation Consumers with at least one credit card have a mean of 4.84 credit cards. [Source: Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson, "Learning in the Credit Card Market," Working Paper 13822, National Bureau of Economic Research (NBER), February 2008.] You want to test the hypothesis that the mean number of credit cards held by low-income consumers (consumers with annual incomes below $20,000) is different from the reported mean of 4.84 A random sample of 300 low-income consumers provides a sample mean number of credit cards of x = 4.50. Use a significance level of = .05 for the test. Use a confidence interval estimate approach to conduct the hypothesis test. 90% 5% 10% 95% confidence To use a confidence interval estimate approach to conduct the hypothesis test, you construct the interval estimate of the population mean.

Explanation / Answer

Following is the output of confidence interval generated by the excel:

90% confidence interval:

4.16 and 4.84

Since confidence interval contains 4.84 so we fail to reject the null hypothesis on the basis of this confidence interval.

5% confidence interval:

4.49 and 4.51

Since confidence interval does not contain 4.84 so we reject the null hypothesis on the basis of this confidence interval.

10% confidence interval:

4.47 and 4.53

Since confidence interval does not contain 4.84 so we reject the null hypothesis on the basis of this confidence interval.

95% confidence interval:

4.10 and 4.90

Since confidence interval contains 4.84 so we fail to reject the null hypothesis on the basis of this confidence interval.

Confidence interval - mean 95% confidence level 4.5 mean 3.56 std. dev. 300 n 1.960 z 0.403 half-width 4.903 upper confidence limit 4.097 lower confidence limit Confidence interval - mean 90% confidence level 4.5 mean 3.56 std. dev. 300 n 1.645 z 0.338 half-width 4.838 upper confidence limit 4.162 lower confidence limit Confidence interval - mean 5% confidence level 4.5 mean 3.56 std. dev. 300 n 0.063 z 0.013 half-width 4.513 upper confidence limit 4.487 lower confidence limit Confidence interval - mean 10% confidence level 4.5 mean 3.56 std. dev. 300 n 0.126 z 0.026 half-width 4.526 upper confidence limit 4.474 lower confidence limit