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3 weeks ago
Graduation tests Many states mandate tests that have to be passed in order for the students to graduate with a high school diploma. A local school superintendent believes that after-school tutoring will improve the scores of students in his district on the state's graduation test. A tutor agrees to work with 15 students for a month before the superintendent will approach the school board about implementing an after-school tutoring program. The after-school tutoring program will be implemented if student scores increase by more than 20 points. The superintendent will test a hypothesis using α = 0.02 .

a. Write appropriate hypotheses (in words and in symbols).
b. In this context, which do you consider to be more serious - a Type I or a Type II error? Explain.
c. After this trial produced inconclusive results, the superintendent decided to test the after-school tutoring program again with another group of students. Describe two changes he could make in the trial to increase the power of the test, and explain the disadvantages of each.
Textbook 

Stats: Modeling the World


Edition: 4th
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3 weeks ago
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a. H0: μ = 20; The difference between the mean number of points before and after the tutoring program is not more than 20.
HA: μ > 20; The difference between the mean number of points before and after the tutoring program is more than 20.
b. A Type I error would be very expensive for the school district. A Type I error would mean that the superintendent thought the tutoring program was working better than it was, so he would implement the program. In reality, the after-school tutoring program did not improve student test scores, so the school district would be spending money on a program that did not help. (Note: Students could argue that a Type II error would be worse.)
c. To increase the power of the test, we could increase the level of significance (α) or increase the sample size. By increasing the level of significance, it could lead to adopting a tutoring program that actually doesn't help. By increasing the sample size, the trial cost would increase.
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