5 It is claimed that \(30 \%\) of packets of Froogum contain a free gift. Andre thinks that the actual proportion is less than \(30 \%\) and he decides to carry out a hypothesis test at the \(5 \%\) significance level. He buys 20 packets of Froogum and notes the number of free gifts he obtains.

1. State null and alternative hypotheses for the test.
2. Use a binomial distribution to find the probability of a Type I error. Andre finds that 3 of the 20 packets contain free gifts.
3. Carry out the test.