CAIE S2 2012 November — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2012
SessionNovember
TopicHypothesis test of binomial distributions
TypeOne-tailed test critical region

4 A cereal manufacturer claims that \(25 \%\) of cereal packets contain a free gift. Lola suspects that the true proportion is less than \(25 \%\). In order to test the manufacturer's claim at the \(5 \%\) significance level, she checks a random sample of 20 packets.
  1. Find the critical region for the test.
  2. Hence find the probability of a Type I error. Lola finds that 2 packets in her sample contain a free gift.
  3. State, with a reason, the conclusion she should draw.