The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to
7,526 hours. The population standard deviation is 1,080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,226 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,526 hours?
b. Compute the p-value and interpret its meaning
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
d. Compare the results of (a) and (c). What conclusions do you reach?
a. Let $\mu$ be the population mean. Determine the null hypothesis, $H_0$, and the alternative hypothesis, $H_1$.
$H_0: \mu = 7526$
$H_1: \mu \neq 7526$
What is the test statistic?
$Z_{STAT} = $ (Round to two decimal places as needed.)