Question

. It has been reported that the average credit card debt for college seniors at the college book store at a college or univerisity is 3262 dollars. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and find that the average debt is 2995 dollars. The population standard deviation (sigma) is 1100 dollars. With an alpha of 0.05, is the student senate correct?

a. Yes b. No

Answer 1

The test hypothesis is


Now, the value of test static can be found out by following formula:


Using Excel's function , the P-value for in an power-tailed t-test with 49 degrees of freedom can be computed as

Since , we reject the null hypothesis in favor of the alternative hypothesis

OR,
Since the sample size is n = 50, degrees of freedom on the t-test statistic are n-1 = 50-1 = 49
This implies that


Since, the t distribution is symmetric about zero, so
Since , we reject the null hypothesis in favor of the alternative hypothesis

YES, The student senate is correct

please thumbs up, if this helped