1.) Suppose the average size of a new house built in a certain county in 2010 was 2,272 square feet. A random sample of 25 new homes built in this county was selected in 2014. The average square footage was 2,190, with a sample standard deviation of 225 square feet.
a. Using a=0.02, does this sample provide enough evidence to conclude that the average house size of a new home in the county has changed since 2010?
b. Estimate the p-value for this test using Table 5 Appendix A attached.
c. Determine the precise p-value for this test using excel.
d. Use PHStat to validate these results.
2. Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. In 2012, 24% of Americans had a credit score below 600. Due to the recent financial crisis, the federal government is concerned that this proportion has increased. To test this hypothesis, a random sample of 250 Americans was chosen in 2014. From this sample, 67 people had credit scores less than 600. Using a = 0.10, answer the following below:
a. Does this sample provide support for the government’s concern that the proportion of Americans with credit scores below 600 has increased since 2012?
b. Determine the p-value for this test.
c. Verify your results using PHStat.