Math  /  Data & Statistics

QuestionCar dealers across North America use the Kelley Blue Book to help determine the value of used cars that their customers trade in when purchasing new cars. However, the Blue Book does not include the car's odometer reading as an indication of the car's value, despite the fact that this is a critical factor for usedcar buyers. It seems reasonable to believe that the more miles a used car has been driven, the less one would be willing to pay for the car. To examine this issue, a used-car dealer randomly samples 100 Toyota Camrys that were sold at auction during the past month. Each car was in top condition, three years old, and equipped with only standard features. The dealer recorded the following two variables: the selling price of the car (in dollars) and the odometer reading (in thousands of miles). StatCrunch was used to create the output below: Parameter estimates: \begin{tabular}{|l|c|c|c|c|c|c|} \hline Parameter & Estimate & Std. Err. & Alternative & DF & T-Stat & P-Value \\ \hline Intercept & 17248.727 & 182.09258 & 0\neq 0 & 98 & & <0.0001<0.0001 \\ \hline Slope & -66.86088 & 4.974639 & 0\neq 0 & 98 & & <0.0001<0.0001 \\ \hline \end{tabular}
Predicted values: \begin{tabular}{|c|c|c|} \hline X value & 95\% C.I. for mean & 95\% P.I. for new \\ \hline 41.672 & (14376.9375,14548.063)(14376.9375,14548.063) & (13808.969,15116.032)(13808.969,15116.032) \\ \hline \end{tabular}
For any numeric responses, round your answers to four decimal places. a. Use the regression equation to provide a point estimate for the selling price of a used Toyota Camry with an odometer reading of 41,672 miles. Note: Be careful of the value you plug into the equation for the mileage - the mileage used to create the model was measured in thousands of miles. y=\mathrm{y}= \square b. The car dealership would like to estimate the average selling price for used Camrys with this odometer reading. Which interval would be the most appropriate to provide? confidence interval prediction interval c. Interpret the interval selected in part b: With 95%95 \% confidence, we estimate the
Select an answer with \square miles is between \square and \square

Studdy Solution
Interpret the confidence interval:
With 95% 95\% confidence, we estimate the average selling price for used Camrys with an odometer reading of 41,672 41,672 miles is between 14376.9375 14376.9375 and 14548.063 14548.063 .
The point estimate for the selling price is:
14461.7365 \boxed{14461.7365}
The appropriate interval is the confidence interval.
Interpretation: With 95% 95\% confidence, we estimate the average selling price for used Camrys with an odometer reading of 41,672 41,672 miles is between 14376.9375 \boxed{14376.9375} and 14548.063 \boxed{14548.063} .

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