TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9, which of the following best describes the Type II error?
A) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower.
B) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher.
C) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower.
D) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

Question

Quizplus · Accepted Answer

A type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, the null hypothesis is that the mean SAT score of this year's entering class is equal to or higher than previous years (μ ≥ 1520). The alternative hypothesis is that the mean SAT score of this year's entering class is lower than previous years (μ < 1520). Therefore, a type II error would occur if the president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower.

TABLE 9-9 The President of a University Claimed That the Entering Class