Bank of America\'s consumer Spending Survey collected data on annual credit card

Question

Bank of America's consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment (U.S. Airways Attache, December 2003). Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries(population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was d = $860, and the sample standard deviation was s_d = $1,126. a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. H_0: mu_d equal to 0 H_a: mu_d not equal to 0 b. Use a. 05 level of significance. What is the p-value? The p-value is less than. 01 Can you conclude that the population means differ? There is a difference between the annual mean expenditures? c. Which category, groceries or dining out, has a higher population mean annual credit card charge? What is the point estimate of the difference between the population means? $ what is the 95% confidence interval estimate of the difference between the population means (to the nearest whole number)?

Explanation / Answer

(c)
point estimate of the difference between the poulation means = $860

for 95% CI, z-value = 1.64
lower bound = 860 - 1126/sqrt(42) = 686.2544
upper bound = 860 + 1126/sqrt(42) = 1033.7456

(686 , 1034)

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