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 $907, 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. * Họ: A = 907 Hu907 | 0 AM > 907 H, # < 907 HON< 907 HA > 907 Hos - 907 Hou < 907 Ho: = 907 H: > 907 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.) p-value-

Answer 1

we have given : ne sample size = 500 (who paid full each month) sample mean $825 S = sample standard deviation $ 200 U= pop wation mean $ got 2=0.01 Clevel of significance) Claim Is these convincing evidence that college students who pay their credit card balance in full

each month have a mean balance that is lower than $ 907 *) state the appropriate null 4 alternative hypothesis Ho: M = gof VS Mi: u < 907. *) Test statistici ta cá-4) * Só S ( 825-gof) * 500 t = 9.,678 19.2 200

Р value = pit <-9.2 = <0.00001 (use technology) Decision - we reject Ho if p value ca value using p value approach here Р value < & value we reject Ho conclusion :- There is sufficient convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $ 907.