Question

What Is Power? The Trial Urban District Assessment (TUDA)
measures educational progress within participating large urban
districts. TUDA gives a reading test scored from 0 to 500. A score of
210 is a “basic” reading level for fourth-graders.6 Suppose scores on
the TUDA reading test for fourth-graders in your district follow a
Normal distribution with standard deviation σ = 40. In 2013, the mean
score for fourth-graders in your district was 220. You plan to give the
reading test to a random sample of 25 fourth-graders in your district
this year to test whether the mean score μ for all fourth-graders in
your district is still above the basic level. You will therefore test
H0: μ = 210
Ha: μ > 210
If the true mean score is again 220, on average, students are
performing above the basic level. You learn that the power of your
test at the 5% significance level against the alternative μ = 220 is
0.346.

(a) Explain in simple language what “power = 0.346” means.
(b) Explain why the test you plan will not adequately protect you
against deciding that average reading scores in your district are
not above basic level.

Answer 1