During the recent 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 2010 were compared to houses built in 2014. A random sample of 45 homes built in 2010 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 2014 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 α = 0.05, perform a hypothesis test to determine if the average home constructed in 2010 was larger than a home built in 2014.
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. Verify your results using PHStat.
e. What assumptions need to be made in order to perform this procedure?