A car rental company is planning to replace its fleet of Chrysler 300s.The company's default option is to purchase a new fleet of the same model, but it is considering switching to a fleet of Ford Taurus SE vehicles.The company's main consideration is the resale value of the vehicles: In particular, the company would like to switch models if the average resale value of a Ford Taurus SE is above $10,000, and otherwise it prefers to stick to the default Chrysler 300s.

The company is preparing to collect data about the resale prices of n = 50 Ford Taurus SE vehicles, and then conduct a hypothesis test:

H0: $10,000

HA: > $10,000

The company will reject the null hypothesis and switch to a fleet of Ford Taurus vehicles if thep-value is less than or equal to 0.05.If thep-value is above 0.05 the company will stick with the Chrysler 300s.

(a) Suppose the company obtains a sample whose sample standard deviation iss= 2,150.How high must the sample mean be in order for the company to switch to a fleet of Ford Taurus vehicles (i.e. to reject the Null Hypothesis by obtaining ap-value of 0.05 or less)?

(b) Now suppose that, in reality, the average resale value of Ford Taurus SE vehicles is actually $10,200 and that the population standard deviation actually is $2,150. (Of course the company would not know this!)The correct decision in this case would be for the company to switch to Ford Taurus vehicles because this average exceeds $10,000.How likely is it that the company will obtain a sample that leads them to (incorrectly) stick with the fleet of Chrysler 300s?