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.

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Answered: A report about how American college…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.