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"23% D History Bookmarks Window Help courses.aplia.com Aplia Resources Aplia: Student Que. Testing A Populati.. Aa Aa E 3. Hypoth. Home Grades Personalized Reviews Discussion Course Materials Hypothesis Tests Graded Assignment | Read Chapter 9 | Back to Assignment Due Sunday 09.10.17 at 11:00 PM Attempts: Keep the Highest:/6 5. 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 high-income consumers (consumers with annual incomes over $100,000) is different from the reported mean of 4.84 A random sample of 220 high-income consumers provides a sample mean number of credit cards of 5.40. Use a significance level of -.05 for the test. Use a confidence interval estimate approach to conduct the hypothesis test. To use a confidence interval estimate approach to cond interval estimate of the population mean the hypothesis test, you construct the confidence Use the Distributions tool to help answer the questions that follow Select a Distribution 0 F7

Explanation / Answer

It is given, alpha=0.05, therefore, to use a confidence interval estimate approach to the hypothesis test, one needs to construct the 95% confidence interval estimate of the population mean. That is alpha=0.05, confedence level=1-alpha=1-0.05=0.95~95%.

The sample size is large, N=220, and population standard deviation, sigma=3.56 is known, therefore, use Z distribution.

The confidence interval estimate is as follows:

xbar+-z(sigma/sqrt N), where, xbar is sample mean, z is z critical at alpha/2 (alpha=0.05, alpha/2=0.025), sigma is population mean, and N is sample size.

=5.40+-1.96(3.56/sqrt 220)

=(4.93,5.87)

Per rule, reject null hypothesis, if the confidence interval doesnot contain the population mean. The confidence interval doesnot contain the population mean, mu=4.84 , the null hypothesis rejected.

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