Consumers with at least one credit card have a mean of 4.84 credit cards. [Sourc

Question

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 520,000) is different from the reported mean of 4.84. A random sample of 100 low-income consumers provides a sample mean number of credit cards of x = 3.95. Use a significance level of alpha = .05 for the test. Use a confidence interval estimate approach to conduct the hypothesis test. To use a confidence interval estimate approach to conduct the hypothesis test, you construct the ____ confidence interval estimate of the population mean. Use the Distributions tool to help answer the questions that follow. Assume that the population standard deviation is known and equal to 3.56, the standard deviation from the NBER study. Use the tool to compute the confidence interval estimate. The confidence interval estimate is ____ to____. Since the confidence interval estimate___, the null hypothesis (that the mean number of credit cards held by low-income consumers is 4.84) is____.

Explanation / Answer

you construct 95% confidence interval

for 95% CI, z=1.96

and std error =std deviation/(n)1/2 =0.356

hence confidence interval =sample mean -/+ z*std error =3.2523 ; 4.6477

since interval estimate include does not include 4.84 , the null hypothesis is rejected

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