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.
State the appropriate null and alternative hypotheses (in dollars). (Enter != for ≠ as needed.)
Find the test statistic. (Round your answer to two decimal places.)
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Null hypothesis: The mean credit card balance for college students who pay their balance in full each month is not lower than $907.
Alternative hypothesis: The mean credit card balance for college students who pay their balance in full each month is lower than $907.
Test statistic:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
= (825 - 907) / (195 / sqrt(500))
= -4.00 (rounded to 2 decimal places)
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