A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime / bar x x ˉ x, with, / bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a =.02, do you have enough evidence to reject the manufacturer's claim?

Question

Tristan Tanner

Mathematics

11 May, 14:47

A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime / bar x x ˉ x, with, / bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a =.02, do you have enough evidence to reject the manufacturer's claim?

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Julianna Andersen · Answer 1

Step-by-step explanation:

1. The null hypothesis contains "equal" sign ("=" or "≥" or "≤"), the alternative hypothesis is the complement to the null hypothesis. The claim is "the mean life of a certain type of light bulb is at least 1000 hours". As the claim contains "≥" sign, it is null hypothesis.

H0: µ ≥ 1000

Alternative hypothesis:

The alternative hypothesis is the complement: "the mean life of a certain type of light bulb is less

than 1000 hours".

Ha: µ < 1000

b. As the alternative hypothesis contains "<" sign, the test is left-tailed. Using α = 0.02, we obtain critical value from standard table of normal distribution:

z0 = - 1.54

Thus, the rejection region for the test statistic is z < - 1.54.