A recipe submitted to a magazine by one of its subscribers states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed.

54 55 58 59 59 60 61 61 62 65

Assume that the baking times follow a normal distribution. a. Construct a 99% confidence interval for the mean baking time b. Test the null hypothesis that the mean baking time is greater than 55 minutes. Use = 0.01.