Question

A community action group has heard complaints that African American and Hispanic students are more likely to be suspended (either in-school or out-of-school) than other students. The superintendent of schools offers to review the files of students in grades 9–12. The school system has 39,000 students in grades 9–12: 58 percent African American, 12 percent Hispanic, and 25 percent White.

What target population would you recommend the superintendent use? Why did you recommend this population? (Note that target population refers to the specific population that the data will represent.)
2. State the alternative hypothesis and the null hypothesis the superintendent should test.
3. If the superintendent tests the hypothesis and makes a Type I error, explain what has happened.
4. If the superintendent tests the hypothesis and makes a Type II error, explain what has happened.
5. Should the superintendent be more concerned about a Type I error or a Type II error? Justify your answer.
6. The superintendent originally set α = 0.05. How can she further decrease the probability of a Type I error? How can she further decrease the probability of a Type II error?

Answer 1

(1) The target population the superintendent to use is: African and Hispanic students, because the objective of the Research Study is to find out the validity of the community group's hearing the complaint that African and Hispanic students re more likely to be suspended (either in school or out of school)

(2)

HA: Alternative Hypothesis:   (Claim)

H0:Null Hypothesis: ,

where refers to the average number of times African and Hispanic students are suspended (either in school or out of school refers to the average number of times other than African and Hispanic students are suspended (either in school or out of school)

(3)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, average number of times African and Hispanic students are suspended (either in school or out of school is less than or equal to the average number of times other than African and Hispanic students are suspended (either in school or out of school). But, the superintendent wrongly concludes that average number of times African and Hispanic students are suspended (either in school or out of school is greater than the average number of times other than African and Hispanic students are suspended (either in school or out of school). The superintendent makes Type I error in this situation. The effect of this wrong conclusion is that the superintendent will make appropriate action to rectify the complaint, whereas in actual situation no action need be taken.

(4)

Type II Error: Failure to rejection of a false null hypothesis.

Suppose in reality, average number of times African and Hispanic students are suspended (either in school or out of school is greater than the average number of times other than African and Hispanic students are suspended (either in school or out of school). But, the superintendent wrongly concludes that average number of times African and Hispanic students are suspended (either in school or out of school is equal to or less than the average number of times other than African and Hispanic students are suspended (either in school or out of school). The superintendent makes Type II error in this situation. The effect of this wrong conclusion is that the superintendent will not be making appropriate action to rectify the complaint, whereas in actual situation, remedial action need to be taken.

(5) The superintendent should be more concerned about Type II error because by making Type II Error the superintendent will not be making appropriate action to rectify the complaint, whereas in actual situation, remedial action need to be taken. The avoiding appropriate action will have worse consequences subsequently.

(6) To decrease the probability of Type I error, decrease from existing 0.05 to a lower value say 0.01. To decrease the probability of Type II error, increase from existing 0.05 to a lower value say 0.10.