A survey collected data on annual credit card charges in seven different categories of expenditures: transportation, gro

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A 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. 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, with population 1 − population 2, the sample mean difference
was d = $860, and the sample standard deviation was sd =
$1,128.
(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.
H0: 𝜇d ≠ 0 Ha: 𝜇d = 0
H0: 𝜇d = 0 Ha: 𝜇d ≠ 0
H0: 𝜇d ≤ 0 Ha: 𝜇d > 0
H0: 𝜇d < 0 Ha: 𝜇d = 0
H0: 𝜇d ≥ 0 Ha: 𝜇d < 0
(b) Calculate the test statistic. (Round your answer to three
decimal places.)
What is the p-value? (Round your answer to four decimal
places.)
Can you conclude that the population means differ? Use a 0.05
level of significance.
The p ≤ 0.05, therefore we cannot conclude that there is a
difference between the annual population mean expenditures for
groceries and for dining out. The p ≤ 0.05, therefore we can
conclude that there is a difference between the annual population
mean expenditures for groceries and for dining out. The p >
0.05, therefore we can conclude that there is a difference between
the annual population mean expenditures for groceries and for
dining out. The p > 0.05, therefore we cannot conclude that
there is a difference between the annual population mean
expenditures for groceries and for dining out.
(c) What is the point estimate (in dollars) of the difference
between the population means? $ What is the 95% confidence interval
estimate (in dollars) of the difference between the population
means? (Round your answers to the nearest dollar.) $ to $ Which
category, groceries or dining out, has a higher population mean
annual credit card charge? The 95% confidence interval ---Select---
zero. This suggests that the category with higher mean annual
expenditure is ---Select--- .