Activity 6: Compare House Prices of Two Areas in Miami
In this activity you are going to compare recently listed house prices in two areas in Greater
Miami by collecting data on your own and analyzing data using StatCrunch.
Part 1. Research question and data collection.
Consider two areas of your interest in the Greater Miami Area (Miami Date, Broward and Palm
Beach counties) by specifying city, or zip code, or neighborhood. For example, “Doral” and
“Kendall”.
1. Specify the areas below:
Area 1 (city/zip code/neightborhood): __________________________
Area 2 (city/zip code/neightborhood): __________________________
Go to www.realtor.com. Search for Area 1. Since the search results are sorted by new listing, we
may consider the first 10 search results as a random sample of recently listed houses in this
area. Fill in the table below with the listing prices of the first 10 results in thousand dollars. For
example, a house listed with $1,050,300 has a record of 1050.3 thousand dollars, so in the cell
you will record “1050.3”. Then repeat for Area 2. If you’d like, you may increase the sample size
by collaborating with other students. As what we have learned, the larger sample is always
better. If you worked with other students in collecting the data, identify them here.
Area1 (thousand dollars) Area 2 (thousand dollars)
Part 2. Use StatCrunch software to find a confidence interval. Answer the following questions.
1. Are the two samples of house prices independent or paired? ________________________
2. Based on the sample sizes, which statistic should we use, Z-statistic or T-statistic?
3. Choose a confidence level ___________. The commonly used levels include 90%, 95%, and
99%.
4. Let StatCrunch do the calculation.
STEP1: Load the data into StatCrunch by the following steps:
a. Copy the columns of “Area1 (thousand dollars)” and “Area 2 (thousand dollars)” in
above table including the header.
b. Launch StatCrunch website via MyLab.
c. Under “My data” choose “Paste data into a form”. Paste the data in the empty box,
check “Use first line as variable names”, and choose “Delimiter:” Tab. Select “Load
data”. You should see two columns of data with 10 rows of each in the worksheet.
STEP2: Find the confidence interval of the difference in mean house price.
a. From the worksheet, go to “Stat -> Z stats/T stats -> Two sample/Paired -> With data”.
Choose Z stats or T stats according to question 3, and choose two sample or paired
according to question 2. Notice that “two sample” in StatCrunch means independent
two sample procedure.
b. Under “sample 1 values in” select “Area1 (thousand dollars)”, and under “sample 2
values in” select “Area2 (thousand dollars)”. Select “Confidence interval”. Input the
level you chose in question 3. Click “Compute!”.
c. Fill in the following table with the output. Round the results in whole numbers.
____% confidence interval results:
μ1 : Mean of Area1 (thousand dollars)
μ2 : Mean of Area 2 (thousand dollars)
μ1 – μ2 : Difference between two means
(with pooled variances)
Difference Sample Diff. Std. Err. DF L. Limit U. Limit
μ1 – μ2
5. Interpret the confidence interval (L.Limit, U.Limit).
Part 3. Use StatCrunch software to perform hypothesis test. Answer the following questions.
6. Choose a significance level α=_______. The commonly used levels include 0.01, 0.05, and
0.10.
7. We want to test if there is a difference in the mean house prices in these two. Denote the
mean of Area 1 by μ1 and the mean of Area 2 by μ2. What are the hypotheses?
Ho:
Ha:
7. Perform the hypothesis test in StatCrunch.
a. Back to the worksheet, go to “Stat -> Z stats/T stats -> Two sample/Paired -> With
data”. Choose Z stats or T stats according to question 3, and choose two sample or
paired according to question 2.
b. Under sample 1 values in select “Area1 (thousand dollars)”, and under sample 2 values
in select “Area2 (thousand dollars)”. Select “Hypothesis test”. Enter the hypotheses
according to question 6. Then click “Compute!”.
c. Fill in the following table with the output. Round to at least 2 decimal places.
Hypothesis test results:
μ1 : Mean of Area1 (thousand dollars)
μ2 : Mean of Area 2 (thousand dollars)
μ1 – μ2 : Difference between two means
(with pooled variances)
Difference Sample Diff. Std. Err. DF T/Z-Stat P-value
μ1 – μ2
8. Based on the p-value from the output (no calculation is needed), at the significance level of
your choice in question 6, what is your decision, to reject Ho or not to reject Ho? Explain.
9. Write a complete conclusion of the hypothesis test.
