the critical region. Is the outcome x = 21.1 a good evidence that the population mean score is greater than 20? %3D

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6. In the past, the mean score of the seniors at South High on the American College Testing
(ACT) college entrance examination has been 20. This year a special preparation course is
offered, and all 43 seniors planning to take the ACT test enroll in the course. The sample
mean of 43 ACT scores is 21.1. The principal believes that the new course has improved
the Students' ACT scores.
(a) Assume that ACT scores are normally distributed with standard deviation o=6. State
the critical region. Is the outcome x = 21.1 a good evidence that the population mean
score is greater than 20?
(b) Find the type II error probability and power of the test if the true population mean
is 22.5 (Hint: in this case H1: u=22.5)
Transcribed Image Text:6. In the past, the mean score of the seniors at South High on the American College Testing (ACT) college entrance examination has been 20. This year a special preparation course is offered, and all 43 seniors planning to take the ACT test enroll in the course. The sample mean of 43 ACT scores is 21.1. The principal believes that the new course has improved the Students' ACT scores. (a) Assume that ACT scores are normally distributed with standard deviation o=6. State the critical region. Is the outcome x = 21.1 a good evidence that the population mean score is greater than 20? (b) Find the type II error probability and power of the test if the true population mean is 22.5 (Hint: in this case H1: u=22.5)
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