Interpreting a Computer Display
In Exercises 9–12, refer...

Question

Interpreting a Computer Display

In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.

Table showing regression equation, sample size, correlation, and prediction intervals for car weight and fuel consumption.

Finding a Prediction Interval For a car weighing 4000 pounds (x = 4000) identify the 95% prediction interval estimate of the highway fuel consumption. Write a statement interpreting that interval.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A study examined the relationship between tire width in units of millimeters and braking distance in units of meters. For a set of sports cars for a tire width of 245 millimeters, the statistical software output produces a 95% prediction interval for braking distance as 39.7. To 49.3 m. What is the 95% prediction interval estimate for braking distance for a car with a 245 millimeter wide tires, and what does this interval mean? Awesome. So it appears for this particular problem we're solving for two separate answers. Our first answer is, what is the 95% prediction interval to estimate for the braking distance for a car with 245 millimeter wide tires? That's our first answer. We're trying to create an estimate value or determine rather an estimate value, and our second answer is we're asked to determine an explanation for what does this interval mean. So now that we know what we're trying to solve for. Our first step that we need to take is we need to note and recall that from the computer output, the 95% prediction interval for a tire width of 245 millimeters. So once again, let's note for a 95% prediction. For tire width, which I'll call it TW for tire width of 245 millimeters, is, once again, this is the breaking interval was 39.7 to 49.3 m. Fantastic. So our second step now, since we had to, now that we know what information, what data we're given to solve this from, our second step is we need to note that we could write our interval as parentheses 39.7.49.3 in parentheses, and then you can write the units meters outside of the parentheses. And our 3rd step now is we need to. Determine our interpretation. So as you should recall and note, we can interpret that we are 95% confident that a car with 245 millimeter tires will have a braking distance between 39.7 to 49.3 m. So that will mean that our final answer or answers, I should say, without a doubt, have to be the following. So once again, our prediction, so once again, we had to figure out our prediction interval is parentheses 39.7.49.3 meters. And as for our interpretation, so what does this interval mean? We can state that we are 95% confident that a car with 245 millimeter wide tires will have a braking distance between 39.7 and 49.3 m. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Regression Analysis

Prediction Interval

Correlation Coefficient

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