Many people claim that they can put a meal on the table in a short period of time. However, an article at USA Today in 2006 reported that people usually spend an average of 40 minutes for preparing dinner. A culinary expert wanted to conduct a study to test the validity of this statement. She selected a random sample of 30 people (male and female) and timed them as they made dinner. Their length of time (in minutes) to prepare and cook dinner is recorded, with the following results:

a)Is there a significant evidence that the population mean time to prepare and cook dinner is more than 40 minutes? Use a hypothesis test with = 0.05 to make an informed decision. Show all steps of the hypothesis test being used with your calculator commands.

a)Find a 95% and confidence interval for the population mean time to cook and prepare dinner. Show your work or calculator commands. What is the margin of error? What can be done to make this margin of error smaller?