Packet-mass conclusions at different significance levels

A cereal producer states that the mean mass of cereal in its packets is \(500\) g. A one-tailed test is carried out. At the \(4\%\) significance level, it is found that there is significant evidence that the population mean mass exceeds \(500\) g. 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 nor false.

1. There is significant evidence at the \(7\%\) significance level that the population mean mass exceeds \(500\) g.

   [2]

2. There is significant evidence at the \(2\%\) significance level that the population mean mass exceeds \(500\) g.

   [2]

3. Suppose instead a two-tailed test is carried out at the \(4 \%\) significance level. There is significant evidence that the population mean mass is not equal to 500 g.

   [2]