4. A company produces sweets of varying colours. The company claims that the proportion of blue sweets is \(13.6 \%\). A consumer believes that the true proportion is less than this. In order to test this belief, the consumer collects a random sample of 80 sweets.

1. State suitable hypotheses for the test.
2. 1. Determine the critical region if the test is to be carried out at a significance level as close as possible to, but not exceeding, \(5 \%\).
   2. Given that there are 6 blue sweets in the sample of 80, complete the significance test.
3. Suppose the proportion of blue sweets claimed by the company is correct. The consumer conducts the sampling and testing process on a further 20 occasions, using the sample size of 80 each time. What is the expected number of these occasions on which the consumer would reach the incorrect conclusion?
4. Now suppose that the proportion of blue sweets is \(7 \%\). Find the probability of a Type II error. Interpret your answer in context.