"In Exercises 19-24, construct the indicated prediction interv...

Question

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.

23. Construct a 99% prediction interval for the top speed of an electric car in Exercise 17 that takes 5.9 seconds to accelerate from 0 to 60 miles per hour."

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 uses the regression equation Y is equal to 30 + 2.5 multiplied by X to predict the cholesterol level Y based on daily fiber intake X in grams, the standard. of estimate is S equals 6.1. The sample size is N is equal to 22. The mean fiber intake is X bar is equal to 18, and S subscript XX is equal to 210. Construct a 99% prediction interval for a person who consumes 25 g of fiber daily. Awesome. So it appears for this particular problem we're ultimately trying to construct a 99% prediction interval for an individual who consumes 25 g of fiber per day. So now that we know that we're ultimately trying to determine what this interval value is based on all the information that is provided to us by the prom itself. Let's read off her multiple choice answers to see what her final answer for the interval might be, noting once again that they're all written in interval notation, so they're all written inside of parentheses. So A is 72.88,112.12. B is 45.21, 67.31. C is 41.6270.91, and finally D is 43.05, 69.57. Awesome. So our first step that we need to take in order to solve this problem is we need to compute the pre predicted cholesterol value. So once again, in order to compute the predicted cholesterol value, we need to take our regression equation Y hat is equal to 30 + 2.5. Supplied by X, but we're told that our value for X in this case is once again since we're trying to construct a 99% prediction interval for a person who consumes 25 g of fiber daily, so that's our value for X is 25. So when we plug in a value of 25 in for X into our regression equation, we will find that Y hat is equal to 92.5. Once again, that's when we plug our expression into our calculator, we will get an answer of 92.5. Fantastic. Our second step now is we need to compute the value of S predicted, which, as we should recall, will be equal to using our equation, and we should recall in plugging in our known variables, we will get that SP or S predicted. is equal to 6.1 multiplied by the square root of 1 + 1 divided by 22 + parentheses 25 minus 18 to the power of 2 divided by 210. So when we plug in that expression into our calculator, we will find that it's approximately equal to 6. 898 when me round to three decimal places. Fantastic. Our third step now is we need to find our critical T value for a 99% confidence. And an N minus 2, which is equal to 20 degrees of freedom. So that will mean that our value for T, which is our way of denoting our critical T value, so our value of T for this particular prompt will be equal to 2.845. Our fourth step now is we need to compute the margin of error, which will denote as E, and the margin of error E is equal to 2.845 multiplied by 6.898, which will be equal to 19.62. Let me round to two decimal places. Fantastic. And our fifth and final step is we need to construct our interval, so we need to take 92.5 plus or minus 19.62, which will be equal to when we round to two decimal places, 72.88, 112.12. Fantastic, we did it. We found our interval, and that's our final answer. Hooray, we did it. So looking at our Multiple choice answers. The correct answer without a doubt will have to be multiple choice answer letter A, which is parentheses once again parentheses 72.88112.12. And that's it. That's our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.
23. Construct a 99% prediction interval for the top speed of an electric car in Exercise 17 that takes 5.9 seconds to accelerate from 0 to 60 miles per hour."

Key Concepts

Prediction Interval

Confidence Level

Regression and Prediction Using Independent Variables

Watch next