"Constructing and Interpreting a Prediction Interval In Exerci...

Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.

21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."

Accepted Answer

Below there today we're going to 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 company predicts employee productivity using the regression equation Y hat equals 30 + 4 multiplied by X, where X is the number of training sessions attended. The standard error of the estimate is S E is equal to 5, the sample size is N equals 25, and the mean number of sessions is X is equal to 6, and the sum of parentheses X I minus X 2 is equal to 300. What is the 95% prediction interval for productivity when X is equal to 10? Awesome. So it appears for this particular problem, based on all the information that is provided to us by the prom itself, we're asked to determine what is the 95% prediction interval for productivity when X is equal to 10. So now that we know we're ultimately trying to solve for this interval value, let's read off our multiple choice answers to see what our final answer might be for the interval, noting that they're all written inside of parentheses. So A is 63.1.96.9. B is 59.2.80.8, C is 66.0.94.0, and D is 70.5.89.5. Awesome. Our first step that we need to take in order to solve for this particular problem is we need to calculate the predicted value. So in using our regression equation, Y is equal to 30 + 4 multiplied by X, but in this case, X is equal to 10, so we need to plug in a value of 10 for X. So when you plug in this equation into our calculator, we will find that it's simply equal to 70. Our second step now is we need to determine the critical value for T to the power of star for a 95% confidence, or actually not a confidence, we need to do for the 95% prediction interval. Or confidence. So once again, we're told that we have, we're trying to find the 95% prediction interval. So once again, in order to do that at this point, we need to find the critical value T for a 95% confidence. And we need to note that N minus 2 is equal to 23 degrees of freedom, which I'll denote degrees of freedom as DF. So that will mean that our value for T to the power of star is equal to 2.069, and we find this table from our T table, which you should have a tea table in your textbook. If not, you can quickly look one up online. So now our third step now is we need to compute the margin of error by recalling and using the following equation. So the margin of error, ME is equal to using values from this particular problem is equal to 2.0. 69 multiplied by 5 multiplied by the square root of 1 + 1 divided by 25 + 10 minus 6 to the power of 2 divided by 300. And when we plug in this long equation into our calculator, making sure we have the proper parenthesis, we will find that it is approximately equal to when we round to one decimal place, 10.8. Fantastic. So now we know that our margin of error is approximately equal to 10.8. Our next step, which is our fourth and final step, is we need to construct our interval. So we need to take 70 plus or minus 10.8. So when we take 70 plus or minus 10.8, we will find that it will be equal to parentheses 59.2. 80. 8 And that is our final answer. Hooray, we did it, and this corresponds to multiple choice answer letter B, which once again is parentheses 59.280.8. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."

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"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."