Question

A manufacturer claims that the mean lifetime, it, of its light bulbs is 44 months. The standard deviation of these lifetimes is 5 months. Fifty bulbs are selected at random, and their mean lifetime is found to be 45 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 44 months? Perform a two-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. р o 1:0 р The null hypothesis: x s ca The alternative hypothesis MO dº Do - OSO The type of test statistic: (Choose one) Cv The value of the test statistics (Round to at least three decimal places.) O х ? The p-value (Round to at least three decimal places Can we conclude that the mean time of light bulbs made by this manufacturer offers from months Yes

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 44
Alternative Hypothesis, Ha: μ ≠ 44

The test statistic is single mean z test

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (45 - 44)/(5/sqrt(50))
z = 1.414

P-value Approach
P-value = 0.157

As P-value >= 0.05, fail to reject null hypothesis.

No, we cannot conclude