Please make sure to use the sample standard deviation Is 80

7) A manufacturer claims that the mean lifetime of its lithium batteries is 1000 hours. A homeowner thinks it may be different from 1000 hours. She randomly selects 36 of these batteries and finds the sample mean lifetime to be 970 hours with a sample standard deviation of 80 hours. Test the manufacturer\'s claim. Use alpha = 0.05. Please make sure to use the sample standard deviation Is 80 hours

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=1000 (i.e. null hypothesis)

Ha: mu not equal to 1000 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(970-1000)/(80/sqrt(36))

=-2.25

It is a two-tailed test.

Given a=0.05, the critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=-2.25 is less than -1.96, we reject the null hypothesis.

So we can conclude that manufacturer\' claim is correct