Statistics question - Type1 error?

Question

Provide an appropriate response.

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 stops all new programs, but in fact retention is on the rise and the programs help.

B. The product of the university's sample size and sample proportion was less than 10.

C. The university sampled all students at the university.

D. The university concludes that retention is on the rise since the retention rate can only increase.

E. The university concludes that retention is on the rise, but in fact the new programs do not help retention.

Answer 1

A Type I Error is rejecting the null hypothesis when the null is true.



the null hypothesis in this case would be:

H0: p ≤ 0.04 vs H1: p > 0.04



the Type I Error is concluding the the proportion is greater than 4% when the true value is less than 4%. This is solution E in the list provided.







Let α be the significance level of the test



consider the following table



_ _ _ _ _ _ Reject H0 _ _ _ _ Fail to Reject H0

H0 is true _ Type I error _ _ _ _ _ ☺ _ _ _

H0 is false _ _ _ ☺ _ _ _ _ _ _ Type II error _





So, a type I error is rejecting H0 when H0 is true, like sending an innocent person to prison

a type II error is letting a guilty person go free after the trial.



P(Type I Error) ≤ α



P(Type II Error) = β



We generally don't work with Type II errors and instead talk about Power



Power = 1 - P(Type II Error) = 1 - β



in developing tests we try to maximize the Power and minimize α.

Answer 2

Type 1 error is the error of rejecting the null hypothesis given that it is actually true.



Therefore the answer is E. The university concludes that retention is on the rise, but in fact the new programs do not help retention.

Answer 3

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