5. In Manuel's restaurant the probability of a customer asking for a vegetarian meal is 0.30 . During one particular day in a random sample of 20 customers at the restaurant 3 ordered a vegetarian meal.

1. Stating your hypotheses clearly, test, at the \(5 \%\) level of significance, whether or not the proportion of vegetarian meals ordered that day is unusually low. Manuel's chef believes that the probability of a customer ordering a vegetarian meal is 0.10 . The chef proposes to take a random sample of 100 customers to test whether or not there is evidence that the proportion of vegetarian meals ordered is different from 0.10.
2. Stating your hypotheses clearly, use a suitable approximation to find the critical region for this test. The probability for each tail of the region should be as close as possible to \(2.5 \%\).
3. State the significance level of this test giving your answer to 2 significant figures.