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Chapter 2: Describing Data: Frequency distribution and Graphic Presentation (P59)
54. Refer to the Real Estate data, which reports information on homes sold in the Venice. Florida area during the last year.
a. Select an appropriate class interval and organize the selling prices into a frequency distribution.
1. Around what values do the data tend to cluster?
2. What is the largest selling price? What is the smallest selling price?
b. Draw a cumulative frequency distribution based on the frequency distribution developed in Part a.
1. How many homes sold for less than $200,000?
2. Estimate the percent of the homes that sold for more than $220,000.
3. What percent of the homes sold for less than $125,000?
c. Write a report summarizing the selling prices of the homes.
Chapter 3: Describing Data: Measures of Central Tendency (P96)
69. Refer to the Rear Estate data, which reports information on homes sold in the Venice, Florida, area during the last year.
a. Determine the mean and the median selling price of the homes. Does one measure of central tendency seem better, or more representative, than the other?
b. Determine the mean and the median number of bedrooms in a typical house. Does one measure of central tendency seem better, or more representative, than the other?
c. Determine the mean and the median number of bathrooms in a typical house. Does one measure of central tendency seem better, or more representative, than the other?
d. Determine the mean and the median distance from the center of the city. Does one measure of central tendency seem better, or more representative, than the other?
Chapter 4: Other Descriptive Measures (P137)
74. Refer to the Real Estate data, which reports information on homes sold in the Venice, Florida, area last year.
a. For the variable selling price:
1. Find the mean, median, and standard deviation.
2. Determine the coefficient of skewness. Is the distribution positively or negatively skewed?
3. Develop a box plot. Are there any outliners? Estimate the first and third quartiles.
4. Write a brief summary of the distribution of selling prices.
b. For the variable “area of the home in square feet”:
1. Find the mean, median, and the standard deviation.
2. Determine the coefficient of skewness. Is the distribution positively or negatively skewed?
3. Develop a box plot. Are there any outliners? Estimate the first and third quartiles.
4. Write a brief summary of the distribution of the area of homes..
Chapter 5: Probability (P188)
104.Refer to the Real Estate data, which reports information on homes sold in the Venice, Florida, area during the last year.
a. Sort the data into a table that shows the number of homes that have a pool versus the number that don’t have a pool in each of the five townships. If a home is selected random, compute the following probabilities.
1. The home is in Township 1 or has a pool.
2. Given that it is in Township 3, that it has a pool.
3. Has a pool and is in Township 3.
b. Sort the data into a table that shows the number of homes that have a garage versus those that don’t have a garage in each of the five townships. If a home is selected at random, compute the following probabilities:
1. The home has a garage.
2. Given that it is in Township 5, that it does not have a garage.
3. The home has a garage and is in Township 3.
4. Does not have a garage or is in Township2.
Chapter 7: The Normal Distribution (P253)
62. Refer to the Real Estate data set, which reports information on homes sold in the Venice Florida, area during the last year.
a. The mean selling price (in $ thousands) of the homes was computed earlier to be $221.10, with a standard deviation of $47.11. Use the normal distribution to estimate the percent of homes selling for more than $280.0. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?
b. The mean distance from the center of the city is 14.629 miles with a standard deviation of 4.874 miles. Use the normal distribution to estimate the number of homes 18 or more miles but less than 22 miles from the center of the city. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?
Chapter 8: Sampling Methods and the central limit Theorem (P295)
42. Refer to the Real Estate data, which reports information on the home sold in the Venice, Florida, area last year.
a. Compute the mean and the standard deviation of the distribution of the selling prices for the homes. Assume this to be the population. Develop a histogram of the data. Would it seem reasonable from this histogram to conclude that the population of selling prices follows the normal distribution?
b. Let’s assume a normal population. Select a sample of 10 homes. Compute the mean and the standard deviation of the sample. Determine the likelihood of finding a sample mean this large or larger from the population.
Chapter 9: Estimation and Confidence Intervals (P326)
63. Refer to the Real Estate data, which reports information on the homes sold in Venice Florida, last year.
a. Develop a 95 percent confidence interval for the mean selling price of the homes.
b. Develop a 95 percent confidence interval for the mean distance the home is from the center of the city.
c. Develop a 95 percent confidence interval for the proportion of homes with an attached garage.
Chapter 10: One-sample Tests of Hypothesis (P373)
62. Refer to the Real Estate data, which reports information on the homes sold in Venice, Florida, last year.
a. A recent article in the Tampa Times indicated that the mean selling price of the homes on the west coast of Florida is more than $220,000. Can we conclude that the mean selling price in the Venice area is more than $220,000? Use the .01 significance level. What is the p-value?
b. The same article reported the mean size was more than 2,100 square feet. Can we conclude that the mean size of homes sold in the Venice area is more than 2,100 square feet? Use the .01 significance level. What is the p-value?
c. Determine the proportion of homes that have an attached garage. At the .05 significance level can we conclude that more than 60 percent of the homes sold in the Venice area had an attached garage? What is the p-value?
d. Determine the proportion of homes that have a pool. At the .05 significance level, can we conclude that more than 60 percent of the homes sold in the Venice area had a pool? What is the p-value?
Chapter 11: Two-sample Tests of Hypothesis
57. Refer to the Real Estate data, which reports information on the homes sold in Venice, Florida, area last year.
a. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes with a pool and homes without a pool?
b. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes with an attached garage and homes without a garage?
c. At the .05 significance level, can we conclude that there is a difference in the mean selling price of homes in Township 1 and Township 2?
d. Find the median selling price of the homes. Divide the homes into two groups, those that sold for more than (or equal to ) the median price and those that sold for less. Is there a diffirence in the proportion of homes with a pool for those that sold at or above the madian price versus those that sold for less than the median price? Use the .05 signaficance level.
Chapter 12: Analysis of Variance (P446)
41. Refer to the Real Estate data, which reports information on the homes sold in Venice, Florida, area last year.
a. At the .02 significance level, is there a difference in the variability of the selling prices of the homes that have a pool versus those that do not have a pool?
b. At the .02 significance level, is there a difference in the variability of the selling prices of the homes with an attached garage versus those that do not have an attached garage?
c. At the .05 significance level, is there a difference in the mean selling price of the homes among the five townships?
Chapter 13: Linear Regression and Correlation (P498)
52. Refer to the Real Estate data, which reports information on homes sold in Venice, Florida, last year.
e. Let selling price be the dependent variable and size of the home the independent variable. Determine the regression equation. Estimate the selling price for a home with an area of 2,200 square feet. Determine the 95 percent confidence interval and the 95 percent prediction interval for the selling price of a home with 2,200 square feet.
f. Let selling price be the dependent variable and distance from the center of the city the independent variable. Determine the regression equation. Estimate the selling price of a home 20 miles from the center of the city. Determine the 95 percent confidence interval and the 95 percent prediction interval for homes 20 miles from the center of the city.
g. Can you conclude that the independent variables “distance from the center of the city” and “selling price” are negatively correlated and that the area of the home and the selling price are positively correlated? Use the .05 significance level. Report the p-value of the test.
Chapter 14: Multiple Regression and Correlation Analysis (P540)
27. Refer to the Real Estate data which reports information on homes sold in the Venice, Florida, area during the last year. Use the selling price of the home as the dependent variable and determine the regression equation with number of bedrooms, size of the house, whether there is a pool, whether there is an attached garage, distance from the center of the city, and number of bathrooms as independent variables.
a. Write out the regression equation. Discuss each of the variables. For example, are you surprised that the regression coefficient for distance from the center of the city is negative? How much does a garage or a swimming pool add to the selling price of a home?
b. Determine the value of R2. Interpret.
c. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?
d. Conduct the global test on the set of independent variables. Interpret.
e. Conduct a test of hypothesis on each of the independent variables. Would you consider deleting any of the variables? If so, which ones?
f. Rerun the analysis until only significant net regression coefficients remain in the analysis. Identify these variables.
g. Develop a histogram or a stem-and-leaf display of the residuals from the final regression equation developed in part (f). Is it reasonable to conclude that the normality assumption has been met?
h. Plot the residuals against the fitted values from the final regression equation developed in part (f) against the fitted values of y. Plot the residuals on the vertical axis and the fitted values on the horizontal axis.
Chapter 15: Chi-Square Tests Application (P576)
35. Refer to the Real Estate data, which reports information on homes sold in the Venice, Florida, area last year.
a. Develop a contingency table that shows whether a home has a pool and the township in which the house is located. Is there an association between the variables “pool” and “township”? use the .05 significance level.
b. Develop a contingency table that shows whether a home has an attached garage and the township in which the home is located. Is there an association between the variables “attached garage” and “township”? Use the .05 significance level.
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