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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Gerhard

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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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