House prices within certain zip code

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Collect your own sample and use it to estimate the mean house price using a confidence interval and test a published estimate using a hypothesis test.

1. Choose a zip code and find a published estimate for the average house price in that zip code. To do so, you can enter “median house price in [zip code]” in Google and the first result should link to zillow.com, where you will find the “Zillow Home Value Index” prominently displayed. Below this value you will see a brief statement indicating that this value has been adjusted on account of seasonal changes, and that some form of outliers were excluded when calculating this value. Nevertheless, we will take this as a given estimate of the mean house price based on prior research (understanding that this is likely not exactly true, but probably close enough at least for the “middle-tier” of house prices).
2. Go to zillow.com and enter in your chosen zip code (the same one as in the previous step). Randomly select at least 30 houses and their estimated housing price listed on the map, taking care to choose an appropriate sampling method (as discussed in Module 1). Record these house prices in a column of data in Excel. Note: You’ll be including screenshot of your data and your output from Excel, so try to organize it in a simple and clear way.
3. Use the data analysis tool in Excel to find a 98% confidence interval estimate of the mean house price in your chosen zip code. Note whether your confidence interval contains the Zillow Home Value Index found in step 1 or not.
4. Construct a hypothesis regarding the Zillow Home Value Index. You choose your own hypothesis, ie. that the mean house price in your chosen zip code is less than, more than, or the same as Zillow’s published Home Value Index. We will use a significance level of 0.05.
5. Find the p-value for the hypothesis test constructed in the the previous step. 6. Write a short technical report following the outline in the Submission Details section below.
• What is your chosen zip code?
• What is the Zillow Home Value Index for your chosen zip code?
• For the analysis outlined in this project to be valid, you need a sample size of at least 30. How many houses did you select?
• Describe your sampling method. What considerations did you make to ensure that your sample is represents all house prices in the chosen zip code? How did you attempt to ensure your selections were made randomly? Are there any potential flaws with you sampling method that you can identify? Do you expect your sample to be biased in a particular way? Explain.
• Report the upper and lower limits of the 98% confidence interval estimate of the mean house price in your chosen zip code, as determined by the data you collected. Indicate how you calculated these upper and lower limits from the Excel output (you can either verbally describe what you did with the numbers, or show your work).
• State whether your confidence interval contains the Zillow Home Value Index or not. Based on this, do you expect that it is plausible, with 98% confidence, that the mean house price in your chosen zip code is equal to the reported Zillow Home Value Index? • Describe your hypothesis test setup. What are your null and alternative hypotheses? What is the p-value? What formula(s) did you use to get the p-value? What formula(s) did you use to get your p-value? What is your conclusion regarding your hypotheses?

 

 

 

 

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