10.44 The COVID-19 pandemic has significantly affected the real estate market in a country where there was a large decline in demand and nationwide home prices dropped to their lowest. To study the impact of the pandemic, a real estate company randomly selected 15 residential units’ prices (in $ thousand) of the same size and location for a certain period before and during the pandemic. The prices before the pandemic provide the sample mean of $655 per unit with a sample standard deviation of $100. The prices during the pandemic provide the sample mean of $412 per unit with a sample standard deviation of $350. The population variances are assumed to be equal, and that assumption should be used for the problem analysis.

a. Use a hypothesis test with a probability of Type I error = 0.05 to determine if there is strong evidence to support the conclusion that the residential unit prices during the pandemic have dropped compared to the prices before pandemic and interpret the results.

b. Under the assumption that the population variances are equal, construct a 95% acceptance interval for the ratio of the sample variances. Do the observed sample variances lead us to conclude that the population variances are the same? Please explain.