SOLUTION: The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard devi

Question 986136: The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.
a) at the 0.05 level of significance, is there evidence that the mean life is different from 375 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

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho=mean is 375
Ha=mean is not 375
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 (350.5,399.5). 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 375, 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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