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. 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= $850, and the sample standard deviation was $1123. 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. b. Use .05 level of significance. Can you conclude that the population means differ? What is the p -value? (to 6 decimals) 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? Round to the nearest whole number. 850 What is the 95% confidence interval estimate of the difference between the population means? Round to the nearest whole number. (n1,n2)=

Answer 1

The test statistic is

df = 40 - 1 = 39

At = 0.05, the critical values are +/- t_0.025,39 = +/- 2.023

Since the test statistic value is greater than the positive critical value(4.787 > 2.023), so we should reject the null hypothesis.

At 0.05 significance level there is sufficient evidence to conclude that the population means differ.

P-value = 2 * P(T > 4.787)

            = 2 * (1 - P(T < 4.787))

           = 2 * (1 - 0.999988)

           = 0.000024

c) Groceries has a higher population mean annual credit card charge.

The point estimate is = 850

At 95% confidence level, the critical value is t^* = 2.023

The 95% confidence interval is