Question

Stats Hw- Please Help

3. A company that manufactures compact fluorescent light bulbs (CFL) claims that they will operate for a mean of 10,000 hours with a level of significance equal to 0.05. An engineer from the company performs a test to validate this claim. The hypotheses are: Null hypothesis: μ = 10,000 hours Alternate hypothesis: μ ≠ 10,000 hours The engineer does accelerated lifetime testing on 50 of these bulbs and finds that the mean lifetime is 9875 hours with a standard deviation of 665 hours. The resulting p-value is 0.095. Assume conditions for necessary for the test are met. Which of the following statements is true?

a. We reject the null hypothesis, since the p-value is greater than the significance level. We have enough evidence to reject the claim that the bulbs will operate for a mean lifetime of 10,000 hours.

b. We fail to reject the null hypothesis, since the p-value is greater than the significance level. We do not have enough evidence to reject the claim that the bulbs will operate for a mean lifetime of 10,000 hours.

c. More information is needed to answer this question.

Answer 1

The hypotheses are:

Null hypothesis: μ = 10,000 hours

Vs

Alternate hypothesis: μ ≠ 10,000 hours

The resulting p-value is 0.095

level of significance equal to 0.05

We reject Ho if the P-value < level of significance.

Here P-value = 0.095 > level of significance = 0.05

So we fail to reject the null hypothesis

Answer:-

b. We fail to reject the null hypothesis, since the p-value is greater than the significance level. We do not have enough evidence to reject the claim that the bulbs will operate for a mean lifetime of 10,000 hours.