A manufacturer claims that the average lifetime of its light

A manufacturer claims that the average lifetime of its lightbulbs is equal to 36 months. A random sample of 64 bulbs has a mean lifetime of 32 months, and the sample standard deviation is 11 months. We will be using a z-test for the population mean at = 0.05 to check the manufacturer’s claim.

Solution

Ho: mean =36

H1: mean not equal to 36

The test statistics is z=(char-mean)/sigma/sqrt(n)=(32-36)/11/sqrt(64)=-2.91

It is two tailed test.

Give alpha=0.05. Critical value for Z(0.025)=-1.96 and 1.96(from table)

Z =-2.91 is less than -1.96 so reject the Ho

So we cannot conclude that average lifetime of its light bulbs is 36