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AP® Statistics

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College Tuition: Testing the Data

APSTAT-EJKUEL

According to the National Center for Education Statistics, the average total tuition, fees, room and board at 4-year colleges and universities was \$$24,706$ in 2013-2014. Mr. Nye believes the average is now higher.

To investigate, he randomly selects one 4-year school from each of the 50 states. He finds the sample average to be \$$25,322$ and the sample standard deviation to be \$$2,375$. There are no outliers in his data.

Does his data provide evidence at the $\alpha = 0.05$ level that the average total tuition, fees, room and board at 4-year​ colleges has increased?

A

No, the $p$-value for the appropriate significance test is $0.07$. Since $0.07 > 0.05$, we do not have sufficient evidence at the $\alpha = 0.05$ level.

B

No, the sample average is only \$$616$ more than the 2013-2014 value. Considering that costs are more than \$$20,000$, this is really not that much money.

C

Yes, the $p$-value for the appropriate significance test is $0.04$, so we have strong evidence to suggest that the cost has increased.

D

Yes, the sample average represents a $2.5\%$ increase over the 2013-2014 costs. Since this is less than $5\%$, our results are statistically significant at the $\alpha = 0.05$ level.

E

Mr. Nye cannot conduct a significance test here since not all conditions are satisfied.