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An agent for a residential real estate company in a large city has the business objective...

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An agent for a residential real estate company in a large cityhas the business objective of developing more accurate estimates ofthe monthly rental cost for apartments. Toward that goal, the agentwould like to use the size of an apartment, as defined by squarefootage to predict the monthly rental cost. The agent selects asample of 25 apartments in a particular residential neighborhoodand collects the following data: Size (square feet) Rent ($) 8501950 1450 2600 1085 2200 1232 2500 718 1950 1485 2700 1136 2650 7261935 700 1875 956 2150 1100 2400 1285 2650 1985 3300 1369 2800 11752400 1225 2450 1245 2100 1259 2700 1150 2200 896 2150 1361 26001040 2650 755 2200 1000 1800 1200 2750 For these data, Syx =194.5953946 and hi = 0.049156908 when X = 1000. *Round finalanswers below to three decimal places. Do not round calculationsuntil the final answer. (a) Construct a 95% confidence intervalestimate of the mean monthly rental for all apartments that are1000 square feet in size. (b) Construct a 95% prediction intervalof the monthly rent for an individual apartment that is 1000 squarefeet in size. (c) Explain the difference in the results in (a) and(b).

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