A special cable has an average breaking strength of 800lbs T

A special cable has an average breaking strength of 800lbs. The standard deviation population is 12lbs. A researcher selects a sample of 21 and finds the average breaking strength is 792lbs. Can he reject the claim that the breaking strength is 800lbs. Use the P-value method a= 0.05 normally distributed

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=800 (i.e. null hypothesis)

Ha: mu not equal to 800 (i.e. alternative hypothesis)

The test statistic is

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

=(792-800)/(12/sqrt(21))

=-3.06

It is a two-tailed test.

So the p-value= 2*P(Z<-3.06) =0.0022 (from standard normal table)

Since the p-value is less than 0.05, we reject the null hypothesis.

So we can not conclude that the breaking strength is 800lbs.