Question

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 $200. 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 $905, the value reported for all college students with credit cards? Carry out a hypothesis test using a significance level of 0.01.

State the appropriate null and alternative hypotheses.

- H₀: μ = 905

H_a: μ > 905

H₀: μ < 905

H_a: μ > 905

    

H₀: μ = 905

H_a: μ ≠ 905

H₀: μ > 905

H_a: μ < 905

H₀: μ = 905

H_a: μ < 905

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t =

P-value =

State the conclusion in the problem context.

We fail to reject H₀. We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

We reject H₀. We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.   

We reject H₀. We do not have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

We fail to reject H₀. We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Answer 1

The statistical software output for this problem is:

From above output:

Hypotheses:

H₀: μ = 905

H_a: μ < 905

t = -8.9

P = 0.000

Conclusion: We reject H₀. We have convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.