ESSENTIAL STATISTICS 2 E William Navidi and Barry
ESSENTIAL STATISTICS 2 E William Navidi and Barry Monk ©Mc. Graw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of Mc. Graw-Hill Education.
Inference About The Response Section 11. 4 ©Mc. Graw-Hill Education.
Objectives 1. Construct confidence intervals for the mean response 2. Construct prediction intervals for an individual response ©Mc. Graw-Hill Education.
Objective 1 Construct confidence intervals for the mean response ©Mc. Graw-Hill Education.
Two Further Problems • ©Mc. Graw-Hill Education.
Intuitive Picture of the Problems • ©Mc. Graw-Hill Education.
Visualizing the Problems • ©Mc. Graw-Hill Education.
Point Estimate • The reason is that there is less variation in the mean of all the values in a vertical strip than in the distribution of the individual points. ©Mc. Graw-Hill Education.
Confidence Interval for the Mean Response • ©Mc. Graw-Hill Education.
Example: Confidence Interval for Mean Response Construct a 95% confidence interval for the mean number of calories for candy products containing 18 grams of fat. ©Mc. Graw-Hill Education.
Example: Confidence Interval for Mean Response (Solution) • ©Mc. Graw-Hill Education.
Interpreting Mean Response In the previous example, we found that we are 95% confident that the mean number of calories for candy products containing 18 grams of fat is between 450. 960 and 465. 534. You are planning to purchase a particular product that contains 18 grams of fat. Can you be 95% confident that the number of calories in your particular product will be between 450. 960 and 465. 534? Explain why or why not. Solution: No, you cannot be 95% confident that the number of calories in your particular product will be between 450. 960 and 465. 534. The confidence interval for the mean response provides information about the mean number of calories for all candy products with 18 grams of fat. To estimate the number of calories in a particular product, we need a prediction interval for an individual response. The prediction interval will have a larger margin of error than the confidence interval for the mean response. ©Mc. Graw-Hill Education.
Objective 2 Construct prediction intervals for an individual response ©Mc. Graw-Hill Education.
Individual Response To estimate the number of calories in a particular product, we need a prediction interval for an individual response. The prediction interval will have a larger margin of error than the confidence interval for the mean response. The reason is that there is more variation in the distribution of the individual points than in the mean of all the values in a vertical strip. ©Mc. Graw-Hill Education.
Prediction Interval for an Individual Response • ©Mc. Graw-Hill Education.
Example: Prediction Interval for an Individual Response A particular candy product has a fat content of 18 grams. Construct a 95% prediction interval for the number of calories in this product. ©Mc. Graw-Hill Education.
Example: Prediction Interval for an Individual Response (Solution) • ©Mc. Graw-Hill Education.
Interpreting Individual Response Refer to the last example. You are planning to eat a candy bar, and you want to consume less than 500 calories. If you choose an item that contains 18 grams of fat, can you be reasonably sure that it will contain less than 500 calories? Solution: Yes. We are 95% confident that a particular candy bar with a fat content of 18 grams will have between 426. 503 and 489. 992 calories. Therefore, we can be reasonably sure that it will contain less than 500 calories. ©Mc. Graw-Hill Education.
You Should Know. . . • How to construct confidence intervals for the mean response • How to construct prediction intervals for an individual response ©Mc. Graw-Hill Education.
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