N2001 P2 Q10

The batteries, used in a particular model of mobile phone, is advertised as having a ‘talk-time’ of \(5\) hours. In a test at the \(5\)% level of significance, it is found that the population mean talk-time is less than \(5\) hours. Using only this information, and giving a reason in each case, state whether each of the following statements is (i) necessarily true, (ii) necessarily false, or (iii) neither necessarily true or necessarily false.

1. There is significant evidence at the \(10\)% significance level that the population mean talk time is less than \(5\) hours.
2. There is significant evidence at the \(5\)% significance level that the population mean talk time is not \(5\) hours.