A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate. Identify the Type I error in this context.
A) The university sampled all students at the university.
B) The product of the university's sample size and sample proportion was less than 10.
C) The university stops all new programs, but in fact retention is on the rise and the programs help.
D) The university concludes that retention is on the rise, but in fact the new programs do not help retention.
E) The university concludes that retention is on the rise since the retention rate can only increase.
WHAT IS THE ANSWER?!
The correct answer is D) The university concludes that retention is on the rise, but in fact the new programs do not help retention.
In statistical hypothesis testing, a Type I error occurs when a null hypothesis is mistakenly rejected, even though it is true. In this scenario, the type I error would be if the university concludes that their new programs have led to an increase in retention rates, when in reality, the programs do not actually help retention.
The Type I error refers to the incorrect rejection of a true null hypothesis. In this context, the null hypothesis would be that the new programs implemented by the university did not have any effect on the retention rate.
Looking at the given options, the Type I error occurs when the university concludes that retention is on the rise (meaning they reject the null hypothesis) even though in reality, the new programs do not help with retention (the null hypothesis is true).
Thus, the correct answer is D) The university concludes that retention is on the rise, but in fact the new programs do not help retention.
Type I or alpha error is the probability of rejecting the null hypothesis when it is actually true.
http://en.wikipedia.org/wiki/Type_I_and_type_II_errors
http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html
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