A real estate agent claims that the mean living area of all single-family homes in his country is at least 2400

A real estate agent claims that the mean living area of all single-family homes in his country is at least 2400

square feet. A random sample of 50 such homes selected from this country produced the mean living area of 2540 square feet and a standard deviation of 472 square feet.

a. Using a significance level of 5%, can you conclude that the real estate agent's claim is true? Use a diagram and show the 5-step method.

b. What would be the probability of committing a Type I Error in this case?