Practice Exam: Hypothesis Testing for Mortgage and Home Sales Prices

This test is open-book, open-note, open-Excel, and open-internet but you are NOT allowed to consult with fellow students or any other people about either the problems or the answers.

For each problem, show at minimum:
1) The null and alternative hypotheses, written using proper notation 
2) The test statistic calculation showing: the letter of the test statistic (t or z), the formula for the test statistic, the numbers filled into the formula, and the final result. Round Ztest test statistics to two decimals; round ttest test statistics to three decimals. 
3) The rejection step showing BOTH the p-value approach (2 points) AND the CV approach (2 points). You do not need to draw the rejection diagram unless you want to. You must show the proper p-value and proper CV, and the rejection rule (whether in numbers or with the diagram) that led you to your decision about the null hypothesis. State what happened to the null and the alternative hypotheses to get full credit.

4) Interpret the test result, referencing the alpha significance level (or percent confidence level), and answering all questions asked. 

Write out your answers and upload them to Canvas by 11:59pm on Friday, Oct 29. If you need to use
extra paper, that is fine, just scan all of your work. If you cannot print this test, that is fine just write your
answers on a separate page and number them.

This portion of the exam will be scored out of 22 total points possible. Partial credit will be awarded if your answers merit it. This portion of the exam is worth 35% of your Exam 1 grade; the multiple choice part will be worth 65% of your Exam 1 grade.

1. Closing costs for mortgages are an important concern for people buying homes. A realtor read an article in an industry publication that stated the mean closing costs for single-family homes in Michigan were $2015. She suspected that closing costs in her county were lower than that.

To test this, the realtor took a random sample of 54 single-family home sales in her county. In the sample, the mean closing costs were $1894 and the standard deviation was $818.
Perform a hypothesis test to determine whether the population mean closing costs in the realtor’s county are lower than the mean in Michigan as a whole. Use an α = 0.05 significance level. Based on these results, can the realtor tell her clients that population mean closing costs are lower than $2015 in her county?

2. The realtor had noticed some recent changes in the sales prices for single-family homes in two cities in her county. While City A and City B had always had similar home prices in the past, recently she had noticed that this might be changing. She decided to use hypothesis testing to see if the population mean home price was different in these two cities.

The realtor took two random, independent samples. In City A, a random sample of 45 single-family homes sold recently had a mean sales price of $194,020. In City B, a random sample of 46 single-family home sold recently had a mean sales price of $173,700. From past experience, the realtor assumed that the population standard deviation of home sales prices was $51,050 in City A, and $40,115 in City B.

Using an α = 0.05 significance level, perform a hypothesis test to determine whether the population mean home sales price in City A is different than City B. Use the home sales in City A as population 1.
Can the realtor conclude that the population mean price in City A is different than in City B? Extra Credit (2 points): without doing another hypothesis test, can she conclude that prices are higher in City A than in City B? Explain how she can tell, or if she can’t, why she cannot.