12 A firm claims that no more than \(2 \%\) of their packets of sugar are underweight. A market researcher believes that the actual proportion is greater than \(2 \%\). In order to test the firm's claim, the researcher weighs a random sample of 600 packets and carries out a hypothesis test, at the \(5 \%\) significance level, using the null hypothesis \(p = 0.02\).
- Given that the researcher's null hypothesis is correct, determine the probability that the researcher will conclude that the firm's claim is incorrect.
- The researcher finds that 18 out of the 600 packets are underweight. A colleague says
" 18 out of 600 is \(3 \%\), so there is evidence that the actual proportion of underweight bags is greater than \(2 \%\)."
Criticise this statement.