A state university annual report showed that its retention rate was at 24% and u

Question

A state university annual report showed that its retention rate was at 24% and university officials would like to increase this rate. After implementing several new programs during the last two years, the university reevaluated its retention rate. Identify a Type I error in the context of this hypothesis test. The university does not conclude that retention is on the rise since the retention rate can only decrease. The university does not conclude that retention rate in increasing, but in fact the retention rate has increased from 24%. The university concludes that retention is on the rise since the retention rate can only increase. The university concludes that retention rate is increasing, but in fact it has not.

Explanation / Answer

Here H0:p=0.24 vs H1:p>0.24

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").

So here Type I error is The universtity concludes that retention rate is increasing, but in fact it has not.

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