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A survey collected data on annual credit card charges in sevendifferent categories of expenditures: transportation, groceries,dining out, household expenses, home furnishings, apparel, andentertainment. Using data from a sample of 42 credit cardaccounts,assume that each account was used to identify the annual creditcard charges for groceries (population 1) and the annual creditcard charges for dining out (population 2). Using the differencedata, with population 1 − population 2, the sample mean differencewas

d = $870,

and the sample standard deviation was

s_d = $1,121.

(a)

Formulate the null and alternative hypotheses to test for nodifference between the population mean credit card charges forgroceries and the population mean credit card charges for diningout.

H₀:μ_d ≠ 0

H_a:μ_d = 0

H₀:μ_d < 0

H_a:μ_d = 0

    

H₀:μ_d ≤ 0

H_a:μ_d > 0

H₀:μ_d ≥ 0

H_a:μ_d < 0

H₀:μ_d = 0

H_a:μ_d ≠ 0

(b)

Calculate the test statistic. (Round your answer to threedecimal places.)

What is the p-value? (Round your answer to four decimalplaces.)

Can you conclude that the population means differ? Use a 0.05level of significance.

The p ≤ 0.05, therefore we can conclude that there is adifference between the annual population mean expenditures forgroceries and for dining out.The p > 0.05, therefore wecan conclude that there is a difference between the annualpopulation mean expenditures for groceries and for diningout.    The p > 0.05, therefore wecannot conclude that there is a difference between the annualpopulation mean expenditures for groceries and for dining out.Thep ≤ 0.05, therefore we cannot conclude that there is adifference between the annual population mean expenditures forgroceries and for dining out.

(c)

What is the point estimate (in dollars) of the differencebetween the population means?

$

What is the 95% confidence interval estimate (in dollars) of thedifference between the population means? (Round your answers to thenearest dollar.)

$  to $

Which category, groceries or dining out, has a higher populationmean annual credit card charge?

The 95% confidence interval  ---Select--- contains iscompletely below is completely above zero. This suggests that thecategory with higher mean annual expenditureis  ---Select--- groceries dining out .