Answer to Question #217259 in Statistics and Probability for Chaeng

Question

In the label, it is written that a light bulb has a mean life of 360 and with a standard deviation of 90 hours. To test the claim, 60 light bulbs were tested and showed a mean life of 354. At the 0.05 significance level, can we say that mean life is different from 360?

Answer 1

$\mu=360 \\ \sigma=90 \\ n=60 \\ \bar{x}=354 \\ H_0: \mu=360 \\ H_1: \mu ≠360$

Test-statistic:

$Z = \frac{\bar{x} - \mu}{\sigma/ \sqrt{n} } \\ Z = \frac{354 - 360}{90 / \sqrt{60}}= -0.516 \\ α=0.05$

Two-tailed test

$Z_{crit}=1.96$

The decision rule is: Reject H₀ if Z ≤ -1.96 or if Z ≥ 1.96.

$Z= -0.516 > Z_{crit} = -1.96$

Accept H₀.

There is enough evidence to conclude that light bulb has a mean life of 360 at the 0.05 significance level.