MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
Bartleby Related Questions Icon

Related questions

Question
100%

A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $195. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $907, the value reported for all college students with credit cards? Carry out a hypothesis test using a significance level of 0.01.

Find the test statistic and P-value.

**Educational Content**

A report examining financial management among American college students provides insights from a survey involving 793 participants. Each participant was questioned about their credit card usage, particularly if they paid their card balance in full each month. Among them, 500 students reported doing so. For these students, the average credit card balance was $825. Although the standard deviation is not provided, it is assumed to be $195 for this exercise.

The research question posed is whether students paying their card balances in full have a mean balance lower than $907, the average for all college students with credit cards. This hypothesis test is conducted with a significance level of 0.01.

**Hypothesis Testing**

*Null and Alternative Hypotheses*

- \( H_0: \mu = 907 \)
- \( H_a: \mu < 907 \)

The selected hypothesis signifies that we are testing if the true mean balance for students who pay in full is less than $907.

**Instructions:**

To complete this exercise, find the test statistic and the P-value. Ensure the test statistic is rounded to one decimal place, and the P-value to three decimal places. Two empty fields are provided to input these values:

- t = 
- P-value = 

This setup provides an opportunity for students to practice using hypothesis testing to draw conclusions from sample data, applying their understanding of statistical significance, mean comparison, and standard deviation.
expand button
Transcribed Image Text:**Educational Content** A report examining financial management among American college students provides insights from a survey involving 793 participants. Each participant was questioned about their credit card usage, particularly if they paid their card balance in full each month. Among them, 500 students reported doing so. For these students, the average credit card balance was $825. Although the standard deviation is not provided, it is assumed to be $195 for this exercise. The research question posed is whether students paying their card balances in full have a mean balance lower than $907, the average for all college students with credit cards. This hypothesis test is conducted with a significance level of 0.01. **Hypothesis Testing** *Null and Alternative Hypotheses* - \( H_0: \mu = 907 \) - \( H_a: \mu < 907 \) The selected hypothesis signifies that we are testing if the true mean balance for students who pay in full is less than $907. **Instructions:** To complete this exercise, find the test statistic and the P-value. Ensure the test statistic is rounded to one decimal place, and the P-value to three decimal places. Two empty fields are provided to input these values: - t = - P-value = This setup provides an opportunity for students to practice using hypothesis testing to draw conclusions from sample data, applying their understanding of statistical significance, mean comparison, and standard deviation.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman