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 the balance in 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 ther convincing evidence that college students who pay the credit card balance in 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 N 907 M 907 M -907 Hyp-907 HA My > 907 MM 907 Mo: < 907 N 907 Find the best st a nd value (Use a table or technology. Round your best to one decimal place and your p-value to the decimal places.) State the conclusion in the problem context. we fail to reject H. We do not have convincing evidence that college students who pay their credit card balance in fuil ach month have a mean balance that is lower than $907 We foto reject 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 $907 we reject. We have convong evidence that college students who pay the credit card in each month have a balance that is lower than $907 We reject Hy we do not have convincing evidence that college students who may their credit card balance in each month have a mean balance that is lower than 907

Answer 1

(first part) right choice

Moix-907 907

here we want to test whether the mean balance is lower than 907, so alternate hypothesis would be Ha: $\mu$ < 907 and opposite of alterante hypothesis would be the null hypothesiss H0:$\mu$$\ge$907.

so right choice would be first H0:$\mu$= 907, Ha: $\mu$ < 907

(second part) statistic t=($\bar{x}$-$\mu$)/(s/$\sqrt n$)=(825-907)/(195/sqrt(50))=-2.9735 with n-1=50-1=49 df

answer is -2.9735

(third part) p-value=P(t<-2.9735)=0.0023 (you can use ms-excel=TDIST(2.9735,49,1))

answer is 0.0023

(fourth part) right choice is third. We Reject H0: We have convincing evidence .............is lower than $907

We reject M. 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