The manager of a large Michelin star restaurant is disappointed with his staff and believes that his chefs are cooking no more than 13 dishes a day. To evaluate this hypothesis, the manager randomly observes the number of dishes that $49$ chefs cook on a random day. He finds that the mean and variance of the number of meals the $40$ chefs cooked is 15 and 4. With these values, the manager runs a statistical test to see if his chefs are making significantly more than 13 dishes a day.