Bank of America\'s Consumer Spending Survey collected data on annualcredit card

Question

Bank of America's Consumer Spending Survey collected data on annualcredit card charges in seven different categories of expenditures:transportation, groceries, dining out, household expenses, homefurnishings, apparel, and entertainment (U.S. AirwaysAttache, December 2003). Using data from a sample of 42 creditcard accounts, assume that each account was used to identify theannual credit card charges for groceries (population 1) and theannual credit card charges for dining out (population 2). Using thedifference data, the sample mean difference was = $855, and the sample standard deviationwas sd = $1200. a.Formulate the null abd alternative hypothesis to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. b.Use a .05 level of significance. Can you can conclude that the population mean differ? what is the p-value? 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?

Explanation / Answer

a) Ho : miu D = 0 Ha : miu D is not 0

t = ( 855 / 1200 / srqtr 42 )

t = 4.62

p value : 0.0001

since p value is lower than level of significance we reject Ho

conclusion there is a difference between the means

95% confidence interval alpha / 2 = 0.025

df = 41 t= 2.021

I: 855 +/- 2.021 * 1200 / srqt 42

855 +/- 374.22

580.78 < miu < 1229.22

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