Question

a light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 765 hours. a random sample of 23 light bulbs has a mean life of 749 hours. assume the population is normally distributed and the population standard deviation is 58 hours. at α = 0.05, do you have enough evidence to reject the manufacturers claim? complete parts (a) through (e).

d. ( h_{0}:mu<749 ) (claim)
( h_{a}:mugeq749 )
e. ( h_{0}:mugeq765 ) (claim)
( h_{a}:mu<765 )
f. ( h_{0}:mu = 749 )
( h_{a}:mu
eq749 ) (claim)

(b) identify the critical value(s). use technology.
( z_{0}=-1.65 )
(use a comma to separate answers as needed. round to two decimal places as needed.)

identify the rejection region(s). choose the correct answer below.

a.

b.

c.

Explanation:

Step1: Determine the type of test

Since \(H_{a}:\mu < 765\), this is a left - tailed test.

Step2: Analyze the rejection region for a left - tailed test

For a left - tailed test with critical value \(z_{0}=- 1.65\), the rejection region is \(z

Answer:

Option B is correct. In a left - tailed test, the rejection region is on the left side of the critical value. The graph in option B shows the "Reject \(H_{0}\)" region on the left side (the shaded part on the left) which is consistent with the left - tailed test (\(H_{a}:\mu < 765\)) and critical value \(z_{0}=-1.65\) (the line on the left side of the mean in the normal distribution curve for option B represents the critical value in a left - tailed test).