Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the sales price of existing homes to fall nationwide (BusinessWeek, March 9, 2009). You would like to see if the data support this conclusion. The file HomePrices contains data on 30 existing home sales in 2006 and 40 existing home sales in 2009.
Click on the webfile logo to reference the data.
1. Provide a point estimate of the difference between the population mean prices for the two years.
2. Develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.
We do not have access to web file.
To answer these questions, you would need to follow these steps:
1. Calculate the mean prices for each year:
- Sum up all the home prices for 2006 and divide by the number of homes sold in that year.
- Sum up all the home prices for 2009 and divide by the number of homes sold in that year.
2. Calculate the point estimate of the difference between the population mean prices for the two years:
Subtract the mean price for 2009 from the mean price for 2006.
3. Calculate the standard deviation for each year:
- Subtract the mean price for each year from each individual home price.
- Square the result from step 2 for each home.
- Sum up all the squared values for each year and calculate the average for each year.
- Take the square root of the average calculated for each year.
4. Calculate the standard error of the difference between the mean prices:
- Square the standard deviation for 2006 and divide it by the number of homes sold in 2006.
- Square the standard deviation for 2009 and divide it by the number of homes sold in 2009.
- Add the two results from the previous steps.
- Take the square root of the result.
5. Calculate the t-value for a 99% confidence interval based on the degrees of freedom:
- The degrees of freedom can be calculated by subtracting 1 from the sum of the homes sold in 2006 and 2009.
- Look up the t-value for a 99% confidence level and the degrees of freedom calculated.
6. Calculate the margin of error:
- Multiply the t-value by the standard error calculated in step 4.
7. Calculate the lower and upper bounds of the 99% confidence interval:
- Subtract the margin of error calculated in step 6 from the point estimate.
- Add the margin of error calculated in step 6 to the point estimate.
After following these steps, you will have the answers to both questions:
1. The point estimate of the difference between the population mean prices for the two years.
2. The 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.