In: Statistics and Probability
An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:
Size (square feet) |
Rent ($) |
850 |
1950 |
1450 |
2600 |
1085 |
2200 |
1232 |
2500 |
718 |
1950 |
1485 |
2700 |
1136 |
2650 |
726 |
1935 |
700 |
1875 |
956 |
2150 |
1100 |
2400 |
1285 |
2650 |
1985 |
3300 |
1369 |
2800 |
1175 |
2400 |
1225 |
2450 |
1245 |
2100 |
1259 |
2700 |
1150 |
2200 |
896 |
2150 |
1361 |
2600 |
1040 |
2650 |
755 |
2200 |
1000 |
1800 |
1200 |
2750 |
For these data, Syx = 194.5953946 and hi = 0.049156908 when X = 1000. *Round final answers below to three decimal places. Do not round calculations until the final answer.
(a) Construct a 95% confidence interval estimate of the mean monthly rental for all apartments that are 1000 square feet in size.
(b) Construct a 95% prediction interval of the monthly rent for an individual apartment that is 1000 square feet in size.
(c) Explain the difference in the results in (a) and (b).