The quality-control manager at a compact fluorescent light bulb (CFL) factory ne
ID: 3362273 • Letter: T
Question
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
7,451 hours. The population standard deviation is100 hours. A random sample of 64 light bulbs indicates a sample mean life of 7,426 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,451 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?
Explanation / Answer
Ho=mean is 7451
Ha=mean is not 7451
alpha=0.05
Test statistic is z=(xbar-mean)/100/(sqrt(64))
critical value is |z|>1.96
calculation is z=25*8/100=+2
Reject Ho. There is a significant difference in the mean life of the population of light bulbs.
CI is 1.96*12.5=24.5 on each side, so it is (7426.5,7476.5).
The value of the sample mean is not in the confidence interval.
the p-value is 0.0456.
This means that if the true mean were 7451, in a sample of 64, we would expect to get this result about 4.56% of the time, below the 5% cut-off we established at the outset.
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