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.
To answer these questions, we need to calculate the point estimate and the confidence interval estimate of the difference between the population mean prices for the two years using the provided data from the "HomePrices" file.
1. To calculate the point estimate of the difference between the two population mean prices, we need to find the sample mean prices for each year and then subtract one from the other.
- Open the "HomePrices" file and find the column or variable that represents the resale prices of houses in 2006.
- Calculate the sample mean of the resale prices for 2006.
- Next, find the column or variable that represents the resale prices of houses in 2009 and calculate the sample mean of these prices.
- Subtract the sample mean of 2006 from the sample mean of 2009 to get the point estimate of the difference between population mean prices for the two years.
2. To develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009, we need to calculate the margin of error and construct the confidence interval.
- Calculate the standard deviation of the sample resale prices for 2006 and 2009.
- Determine the sample sizes of both years.
- Calculate the standard error, which is the standard deviation divided by the square root of the sample size for each year.
- Next, calculate the critical value (Z) associated with a 99% confidence level. This critical value can be found in the Z-table or using statistical software.
- Compute the margin of error by multiplying the critical value by the standard error.
- Finally, construct the confidence interval by subtracting the margin of error from the point estimate and adding the margin of error to the point estimate.
Remember, the specific steps and calculations might vary based on the dataset format and software you are using.