Question4) Refer to the scenario listed in #1 (High School A standardized test s
ID: 3225040 • Letter: Q
Question
Question4) Refer to the scenario listed in #1 (High School A standardized test scores).
a) Assume that you are told that High School A’s performance is not significantly better than the national average. Furthermore, regardless of your results, assume that you rejected the null hypothesis. In this case, did you make an error? If so, what kind was it, and what was the likelihood of this occurrence?
b) In a different scenario, assume that High School A’s performance is significantly better than the national average. Furthermore, regardless of your results, assume that you failed to reject the null hypothesis. In this case, did you make an error? If you are told that the power of this test was 0.86, then what was the likelihood of you making this particular type of error?
Explanation / Answer
a) Type I error is defined as the event of rejecting the true null hypothesis, and as in this case as we are rejecting the null hypothesis regardless of our results, the probability or the likelihood of the type I error would be the probability that the null hypothesis is true and it is still rejected.
b) Type II error is defined as the event of accepting the false null hypothesis, and as in this case as we are accepting the null hypothesis regardless of our results, the probability or the likelihood of the type II error would be the probability that the null hypothesis is false and it is still accepted.
The power of the test is the probability of rejecting the false null hypothesis. As we are given that probability of rejecting the false null hypothesis is 0.86, therefore the probability of type II error would be = 1- Power of the test that is 0.14. Therefore the probability of accepting the false null hypothesis that is the probability of type II error would be 0.14.
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