Years Sales 1 80 3 97 4 92 4 102 6 103 8 111 10 119 10 123 11 117 13 136
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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Question
Years | Sales |
1 | 80 |
3 | 97 |
4 | 92 |
4 | 102 |
6 | 103 |
8 | 111 |
10 | 119 |
10 | 123 |
11 | 117 |
13 | 136 |
You may need to use the appropriate appendix table or technology to answer this question.
The data on y = annual sales ($1,000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation
ŷ = 80 + 4x.
For these data,
x = 7,
Σ(xi − x)2 = 142,
and
s = 4.6098.
(a)
Develop a 95% confidence interval for the mean annual sales (in thousands of dollars) for all salespersons with nine years of experience. (Round your answers to two decimal places.)
$ thousand to $ thousand
(b)
The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales (in thousands of dollars) for Tom Smart. (Round your answers to two decimal places.)
$ thousand to $ thousand
(c)
Discuss the differences in your answers to parts (a) and (b).
The prediction interval is wider than the confidence interval, because you use a different critical value when developing a prediction of the annual sales for one new salesperson with nine years of experience than when developing an estimate of the mean annual sales for all salespersons with nine years of experience.
The confidence interval is wider than the prediction interval, because there is less variability associated with predicting annual sales for one new salesperson with nine years of experience than there is with estimating the mean annual sales for all salespersons with nine years of experience.
The confidence interval is wider than the prediction interval, because you use a different critical value when developing a prediction of the annual sales for one new salesperson with nine years of experience than when developing an estimate of the mean annual sales for all salespersons with nine years of experience.
The prediction interval is wider than the confidence interval, because there is more variability associated with predicting annual sales for one new salesperson with nine years of experience than there is with estimating the mean annual sales for all salespersons with nine years of experience.
The prediction interval is wider than the confidence interval, because confidence intervals are used to predict values of y for new observations corresponding to given values of x, and prediction intervals give an estimate of the mean value of y for a given value of x.
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