Question

• Math SAT scores (Y ) are normally distributed with a mean of 500 and a standard deviation

of 100. An evening school advertises that it can improve students’ scores by roughly a

third of a standard deviation, or 30 points, if they attend a course which runs over several

weeks. The statistician for a consumer protection agency suspects that the courses are

not effective. She views the situation as follows: H0 : E(Y ) = 500 vs. H1 : E(Y ) = 530.

The consumer protection agency wants to evaluate this claim by sending 50 students to

attend classes. One of the students becomes sick during the course and drops out.

(Q4) What is the distribution of the average score of the remaining 49 students under the null,

and under the alternative hypothesis?

(Q5) Compute the power of the test.

(Q6) What options does the statistician have for increasing the power in this situation without

changing its size?

Answer 1

Q6: Increase the sample size for increasing the power without changing the size of the test.