State university uses thousands of fluorescent light bulbs each year. The brand of bulb it currently used has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the branch the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new branch if, when tested, the evidence supports the manufacturer's claim at the .05 significance level. Suppose 121 bulbs were tested with the following results: =827.5 hours, s=100 hours. Conduct the test using α=.05.

 

Sample size ( number or bulbs tested), n= 121

Sample mean, x-bar= 827.5

Sample standard deviation, s= 100

Hypotheses:

Null Hypothesis: Ho: μ= 800

Alternative Hypothesis: Ha: μ > 800 (claim)

Test to be used:

Upper-tailed z-test

Test statistic:

z-score= (x-bar - μ) / (s/√n)

= (827.5 - 800) / (100/√121)

= 27.5 / (100/11)

= 3.025

P-value = P(z>3.025) = 0.001

Decision:

P-value < 0.05 the significant level, reject Ho.

Conclusion:

The university needs to buy new brand of fluorescent light bulbs, since the is a statistical evidence of the claim that new brand of fluorescent light bulbs that cost the same as the branch of university currently uses has more than 800 mean life at the level of significant α= 0.05.