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     = $867, and the sample standard deviation was sd = $1,170. 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. H0: d Ha: d

Answer 1

Let U1= population mean grocery expenditures, U2= population mean dining-out expense

The null hypothesis, H0: d = 0 where d = U1-U2 (difference of mean)

The alternate hypothesis, Ha: d is not equal to zero

T-statistic = (d- Ud) / Sd / sqrt (n)

where d = 867 , Sd = 1170 , n=42, Ud = 0

T-statistic = (867-0) / (1170/sqrt (42) = 4.80

degree of freedom, df=n-1 = 41

p-value = 0.0001 from Test statistic 4.80 at 41 Degree of freedom

Since test-statistic is less than significance value we accept alternate hypothesis i.e. there is a difference between the annual mean expenditures.