Garry Stewart Real Estate Agency advertises that their mean selling time of residential homes is 42 days or less. A competing agency, Steven H Jas, claims that Garry Stewart has a mean selling time of greater than 42 days.

Assume that the standard deviation for selling time on residential homes is 12 days. A sample of 36 recent sale shows a mean selling time of 46 days.

a) Test the competing agency's claim at a 5% level of significance.

b) Discuss what is meant by a type I Error.

c) Discuss what is meant by a type II Error.

d) Explain the Central Limit Theorem.