Question

A company medical director failed to find significant evidence that the mean blood pressure of a population of executives differed from the national mean µ = 128. The medical director now wonders if the test used would detect an important difference if one were present. For a random sample of size 72 from a normal population of executive blood pressures with standard deviation σ = 15, the z statistic is z = (¯x − 128)/(15/ √ 72) The two-sided test rejects H0 : µ = 128 at the 5% level of significance when |z| ≥ 1.96.

(a) . Find the power of the test against the alternative µ = 135.

(b) . Find the power of the test against µ = 121. Can the test be relied on to detect a mean that differs from 128 by 7?

(c) (1 mark). If the alternative were farther from H0, say µ = 138, would the power be higher or lower than the values calculated in (a) and (b)?

Answer 1

The power of the two sided test is

a) Here . The power of the test is

b) Here . The power of the test is

Since the power is high, we can rely on the test.

c) Here . The power of the test is higher than that in  (a) and (b).