1. The manager decides to increase her random sample to include $n+4$ games. She suspects that the actual proportion of games won by teams in red is lower than 0.6.

(i) Using a 5% level of significance, find the critical region for a one-tailed hypothesis test. State your hypotheses clearly.

(ii) Describe, in context, what a Type I error would be and find the probability the test results in a Type I error.

(iii) Using a 10% level of significance, find the largest number of games that could be won by teams wearing red without the test resulting in a possible Type II error.