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.
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just give us the solution please
To provide a point estimate of the difference between the population mean prices for the two years, we need to calculate the mean prices for both 2006 and 2009, and then calculate the difference between the two means.
1. Calculate the mean price for 2006:
- Add up all the sale prices for 2006 homes.
- Divide the sum by the number of homes sold in 2006 (30 homes).
2. Calculate the mean price for 2009:
- Add up all the sale prices for 2009 homes.
- Divide the sum by the number of homes sold in 2009 (40 homes).
3. Calculate the difference between the two means:
- Subtract the mean price for 2006 from the mean price for 2009.
The result will be the point estimate of the difference between the population mean prices for the two years.
To develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009, we can use the following formula:
Confidence Interval = Point Estimate ± (Critical Value * Standard Error)
1. Point Estimate: The difference between the mean prices calculated in the previous step.
2. Critical Value: Look up the critical value for a 99% confidence interval in a t-table or use a statistical software.
3. Standard Error: Calculate the standard error using the formula:
Standard Error = √[(Variance2006/n2006) + (Variance2009/n2009)]
- Variance2006: Calculate the variance of the 2006 prices (subtract the mean price for each home in 2006 from the mean price for 2006, square the result, and sum them up. Divide the sum by n-1, where n is the number of homes sold in 2006).
- Variance2009: Calculate the variance of the 2009 prices (similar to the calculation for 2006 but using the 2009 prices).
- n2006: The number of homes sold in 2006.
- n2009: The number of homes sold in 2009.
Once you have calculated the confidence interval using the formula, you will have a range of values within which we can be 99% confident that the true population mean difference lies.
To answer the first question, we need to find a point estimate of the difference between the population mean prices for the two years.
Step 1: Calculate the sample means of the two groups
- Calculate the mean price of existing homes in 2006 from the data in the HomePrices file.
- Calculate the mean price of existing homes in 2009 from the data in the HomePrices file.
Step 2: Calculate the difference between the two sample means
- Subtract the mean price of existing homes in 2006 from the mean price of existing homes in 2009.
The result of this calculation will be the point estimate of the difference between the population mean prices for the two years.
To answer the second question, we need to develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.
Step 1: Calculate the standard deviations of the two groups
- Calculate the standard deviation of the resale prices of houses in 2006 from the data in the HomePrices file.
- Calculate the standard deviation of the resale prices of houses in 2009 from the data in the HomePrices file.
Step 2: Calculate the standard error of the difference between the two sample means
- Divide the standard deviation of the resale prices of houses in 2006 by the square root of the number of observations in 2006.
- Divide the standard deviation of the resale prices of houses in 2009 by the square root of the number of observations in 2009.
- Calculate the square root of the sum of the squares of the results from the previous calculations.
Step 3: Calculate the margin of error
- Multiply the standard error by the appropriate value from the t-distribution for a 99% confidence level and the degrees of freedom (sum of the number of observations in 2006 and 2009 minus 2).
Step 4: Calculate the confidence interval
- Subtract the margin of error calculated in step 3 from the point estimate calculated in question 1 to get the lower bound of the confidence interval.
- Add the margin of error calculated in step 3 to the point estimate calculated in question 1 to get the upper bound of the confidence interval.
The resulting interval will be the 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.