The quality-control manager at a lightbulb factor needs to determine whether the

Question

The quality-control manager at a lightbulb factor needs to determine whether the mean life of a large shipment of lightbulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 lightbulbs indicates a sample mean life of 350 hours.

At the 0.05 level of significance is there evidence that the mean life is different from 375 hours?

Compute the p-value and interpret its meaning.

Construct a 95% confidence interval estimate of the population mean life of the lightbulbs.

Explanation / Answer

Here Ho: mu =375 vs H1: mu not equal to 375

As n>30 we will use z distribution

Z=xbar-mu/(sd/sqrt(n))=350-375/(100/9)=-1.5

The P-Value is 0.133614 for alpha =0.05

Here we can see that p value>alpha so we do not reject the null hypothesis

So mean life of a large shipment of lightbulbs is equal to 375

Now to find CI, z=1.96

Margin of error =z*sd/sqrt(n)=1.96*100/8=24.5

So CI=mean+/-E=350+/-24.5=(325.5,374.5)

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