Batteries of type A are known to have a mean life of 150 hours. It is required to test whether a new type of battery, type B, has a shorter mean life than type A batteries.

(a) Give a reason for using a sample rather than the whole population in carrying out this test. [1]

A random sample of 120 type B batteries are tested and it is found that their mean life is 147 hours, and an unbiased estimate of the population variance is \(225\text{ hours}^2\).

(b) Test, at the 2% significance level, whether type B batteries have a shorter mean life than type A batteries. [5]

(c) Calculate a 94% confidence interval for the population mean life of type B batteries. [3]