2 Jacques is a chef. He claims that \(90 \%\) of his customers are satisfied with his cooking. Marie suspects that the true percentage is lower than \(90 \%\). She asks a random sample of 15 of Jacques' customers whether they are satisfied. She then performs a hypothesis test of the null hypothesis \(p = 0.9\) against the alternative hypothesis \(p < 0.9\), where \(p\) is the population proportion of customers who are satisfied. She decides to reject the null hypothesis if fewer than 12 customers are satisfied.
- In the context of the question, explain what is meant by a Type I error.
- Find the probability of a Type I error in Marie's test.