In 2009,the average final exam score for students in an introductory math course was 75%.Five years later,a teacher wants to perform a hypothesis test to determine whether the average score of students the course has changed from the 2009 mean of 75%.The hypotheses are: H0: μ = 75%
HA: μ ≠ 75%
Explain the result of a Type II error.

A) The teacher will conclude that the average final exam score in the course has decreased when in fact it is the same.
B) The teacher will conclude that the average final exam score in the course has increased when in fact it is the same.
C) The teacher will not conclude that the average final exam score in the course is different when in fact it is different.
D) The teacher will conclude that the average final exam score in the course is different when in fact it is the same.
E) The teacher will conclude that the average final exam score in the course is the same when in fact it is the same.

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Michael Stephen · Accepted Answer

Final Answer : C, Explanation :  A Type II error occurs when the null hypothesis (H0) is not rejected, even though it is false. In this case, it would mean that the teacher fails to conclude that the average final exam score in the course is different from 75%, even though it has actually changed. This would be a missed opportunity to identify and address any changes that may have occurred in the course over the past five years. Options A, B, and D are incorrect because they suggest that the teacher would draw incorrect conclusions about the average final exam score, while option E does not provide any information on the likelihood of a Type II error occurring.

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