Question

For the given significance test, explain the meaning of a Type II error.

A certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation. The academic director is concerned that market factors may have adversely affected the full-time placement rate and decides to perform a Hypothesis Test to see if her concern is warranted.
H0 : p=0.87
H1: p<0.87
In this situation, explain the meaning of a Type II error.

Answer 1

A Type II error occurs when a false null hypothesis is not rejected. In this given scenario, it means there is not enough evidence to conclude that the full-time placement rate is lower than 87% when, in fact, it is lower.

Step-by-step explanation:

A Type II error occurs when a false null hypothesis is not rejected. In this given scenario, the null hypothesis is that 87% of the academic program's graduates find full-time employment in their field within the first year of graduation. The alternative hypothesis is that the placement rate is less than 87%.

If the academic director fails to reject the null hypothesis (H0: p = 0.87) in the hypothesis test, it means there is not enough evidence to conclude that the full-time placement rate is lower than 87%. However, in reality, if the placement rate is actually lower than 87%, the director would have made a Type II error by not rejecting the false null hypothesis.