2. Captain Ben flies small passenger jets. These jets carry 50 passengers, plus their luggage. On a full flight, these jets will perform properly as long as the total weight of all passengers' checked baggage does not exceed an average weight of 55 pounds. Ben is concerned that passengers on a particular flight have brought unusually heavy bags. He selects a random sample of 10 passengers and weighs their checked baggage. Based on the results from this sample, he must decide whether it is safe to take off.

a) Ben wants to perform a test to determine whether the mean weight of passengers' luggage on this flight is too heavy. State the appropriate null and alternative hypotheses.

b) Describe the two types of errors that you might make. Identify which is a Type I error and which is a Type II error.

c) Explain the consequences of each type of error. Which is the most serious?

d) During his test, the sample mean he found those 10 bags to be was 59 lbs with a standard deviation of 2. Based on an alpha of .05 what choice should be made and what type of error could be created. .