Question

State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. Suppose 121 bulbs were tested with the following results: Conduct the test using

a = .05

Answer 1

This question is incomplete. X-bar and standard deviation S values are missing in the interpretation

so i would give as an example X-bar value as 827.5 and S = 110 and proceed further.

Steps:

H₀: µ = 800 vs H_a : µ > 800

The test statistic is Z = X-bar - µ₀ / (σ / sqrt (n)) = X-bar - µ₀ / (s / sqrt (n) )

= 827.5 - 800 / (110 / sqrt(121)) = 2.75

since the test statistic is greater than 1.645 , H₀ can be rejected. There is sufficient evidence to indicate the average life of the new bulbs exceeds 800 hours when testing at alpha = .05