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 address the first question, we need to calculate the point estimate of the difference between the average home prices in 2006 and 2009.

To get this point estimate, you need to calculate the mean of the home prices for both years and then find the difference between the two means.

Here are the steps to calculate the point estimate:

1. Access the HomePrices data file, either by clicking on the webfile logo mentioned in the question or by obtaining the file from the source provided.

2. Identify the home prices for the years 2006 and 2009 in the data file.

3. Calculate the mean of the home prices for 2006 and 2009 separately.

Mean for 2006: Add up all the home prices for 2006 and divide the sum by the number of observations.

Mean for 2009: Add up all the home prices for 2009 and divide the sum by the number of observations.

4. Subtract the mean for 2006 from the mean for 2009 to obtain the point estimate.

This point estimate will give you an idea of how much the average home price changed between 2006 and 2009.

Moving on to the second question, we need to calculate a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.

To determine this confidence interval, you can follow these steps:

1. Calculate the sample mean and sample standard deviation of the home prices in 2006 and 2009.

2. Use the t-distribution to find the critical value for a 99% confidence level. The number of degrees of freedom in this case is the smaller sample size minus 1.

3. Calculate the standard error of the difference between the means using the following formula:

Standard Error = sqrt((s1^2/n1) + (s2^2/n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for 2006 and 2009, respectively.

4. Multiply the standard error by the critical value obtained in step 2 to get the margin of error.

5. Finally, construct the confidence interval by subtracting the margin of error from the point estimate and adding it to the point estimate.

This confidence interval will provide a range within which we can reasonably estimate the difference between the average home prices in 2006 and 2009 with 99% confidence.