A realty company took a survey of 24 homes and found that the homes had an average area ( in square feet) of 2350 square feet with the standard deviation of 235 square feet. Can you conclude that all the homes in that region has a mean square footage greater than 2200 square feet, at the level of significance 0.05? Use the method of testing hypotheses to arrive at the conclusion. Assume that the areas of homes follow a normal distribution.

What is the distribution of the test statistics?