Question

Let μ denote the mean lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of

H₀: μ = 10

versus

H_a: μ < 10

will be based on a sample of size 36. Suppose that σ is known to be 0.6, so

σ_x = 0.1.

The appropriate test statistic is then

z =

x − 10

0.1

(a)

What is α for the test procedure that rejects

H₀

if

z ≤ −1.38?

(Round your answer to four decimal places.)

α =

(b)

If the test procedure of part (a) is used, calculate β when μ = 9.8. (Round your answer to four decimal places.)

β =

(d)

What is the power of the test when μ = 9.8? (Round your answer to four decimal places.)

When μ = 9.5? (Round your answer to four decimal places.)

Answer 1