Question

The average undergraduate cost per tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? (Remember to follow the steps in hypothesis testing)

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Answer to a math question The average undergraduate cost per tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? (Remember to follow the steps in hypothesis testing)

Expert avatar
Gerhard
4.5
43 Answers
The null hypothesis: \mu=26025 , Then the mean cost is the same as the alternative hypothesis: \mu\gg\:26025 , the mean cost has increased t=\frac{\left(barx-\mu\right)}{\left(\frac{\sigma}{\sqrt{n}}\right)}=\frac{\left(27690-26025\right)}{\left(\frac{5492}{\sqrt{40}}\right)}=1.917 df=40-1=39 using a t-score calculator p-value = 0.0313 Since the p-value < 0.05, we reject the null hypothesis. Therefore, the cost has increased.

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