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 d : $829, and the sample standard deviation was sd = $1,087. 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. Ho: µ d equal to 0 Ha: u d not equal to 0 b. Use a .05 level of significance. What is the p-value? The p-value is less than .01 Can you conclude that the population means differ? There is a difference between the annual mean expenditures c. Which category, groceries or dining out, has a higher population mean annual credit card charge? Groceries 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 (to the nearest whole number)?
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 d : $829, and the sample standard deviation was sd = $1,087. 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. Ho: µ d equal to 0 Ha: u d not equal to 0 b. Use a .05 level of significance. What is the p-value? The p-value is less than .01 Can you conclude that the population means differ? There is a difference between the annual mean expenditures c. Which category, groceries or dining out, has a higher population mean annual credit card charge? Groceries 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 (to the nearest whole number)?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![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 \( \bar{d} = \$829 \), and the sample standard deviation was \( sd = \$1,087 \).
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.
- **Ho:** \( \mu_d \) equal to 0
- **Ha:** \( \mu_d \) not equal to 0
b. Use a 0.05 level of significance. What is the *p*-value?
- The *p*-value is less than 0.01.
Can you conclude that the population means differ?
- There is a difference between the annual mean expenditures.
c. Which category, groceries or dining out, has a higher population mean annual credit card charge?
- **Groceries**
What is the point estimate of the difference between the population means?
- [To be filled]
What is the 95% confidence interval estimate of the difference between the population means (to the nearest whole number)?
- ([To be filled], [To be filled])](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd36b6842-f013-4a5d-8d88-3ce050696fab%2Fcb0eabf8-aedc-4fd3-aac3-07c6e5fb54b7%2Fhz2a175_processed.png&w=3840&q=75)
Transcribed Image Text: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 \( \bar{d} = \$829 \), and the sample standard deviation was \( sd = \$1,087 \).
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.
- **Ho:** \( \mu_d \) equal to 0
- **Ha:** \( \mu_d \) not equal to 0
b. Use a 0.05 level of significance. What is the *p*-value?
- The *p*-value is less than 0.01.
Can you conclude that the population means differ?
- There is a difference between the annual mean expenditures.
c. Which category, groceries or dining out, has a higher population mean annual credit card charge?
- **Groceries**
What is the point estimate of the difference between the population means?
- [To be filled]
What is the 95% confidence interval estimate of the difference between the population means (to the nearest whole number)?
- ([To be filled], [To be filled])
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