During the 2007–2008 decline in the housing market, it appeared that the average size of a newly constructed house fell. To investigate this trend, the square footages of a random sample of houses built in 2008 were compared to houses built in 2018. A random sample of 45 homes built in 2008 had a sample mean of 2,462.3 square feet and a sample standard deviation of 760.8 square feet. A random sample of 40 homes built in 2018 had a sample mean of 2,257.0 square feet and a sample standard deviation of 730.2 square feet. Assume that the population variances for the square footages of houses built in these two years are equal.

a. Using a = 0.05, perform a hypothesis test to determine if the average home constructed in 2010 was larger than a home built in 2018.

b. Construct a 95% confidence interval to estimate the average difference in the square footages of new homes constructed in these two years. Interpret your result.

c. Determine the precise p-value using Excel and interpret the results.

d. What assumptions need to be made in order to perform this procedure?