Behavioral intervention treatments may affect perceptions of reward in human brains, and thus help people to manage weight loss. In one of the first studies relating brain activity related to rewards and weight loss, researchers recorded brain activity associated with rewards as subjects viewed images of high-calorie (HC) foods and images of low-calorie (LC) foods.† The data in the following table are consistent with graphs in the research article. Eight adult Americans enrolled in the study had their brain activity assessed before and after completing a 24-week weight loss program. The data values represent the change in brain activity associated with high-calorie foods, the change in brain activity associated with low-calorie foods, and the difference, HC − LC, for each of the eight subjects. If the weight loss program is effective, then a greater change for the HC treatment would be anticipated, on average, compared to the change for the LC treatment. For purposes of this exercise, you can assume that these eight adults are representative of adult Americans. Subject ID 1 2 3 4 5 6 7 8 HC 4.3 2.1 4.4 2.4 1.4 2.1 2.0 2.9 LC −5.8 −3.1 −2.0 0.4 0.5 1.3 −2.8 −0.3 Difference 10.1 5.2 6.4 2 0.9 0.8 4.8 3.2 Use the Shiny app "Bootstrap Confidence Interval for the Difference in Two Population Means Using Paired Samples" with a minimum of 1,000 samples to construct a 95% bootstrap confidence interval to estimate the mean difference in change in brain activity, HC − LC. (Use ?d = ?HC − ?LC. Round your answers to three decimal places.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Behavioral intervention treatments may affect perceptions of reward in human brains, and thus help people to manage weight loss. In one of the first studies relating brain activity related to rewards and weight loss, researchers recorded brain activity associated with rewards as subjects viewed images of high-calorie (HC) foods and images of low-calorie (LC) foods.† The data in the following table are consistent with graphs in the research article.

Eight adult Americans enrolled in the study had their brain activity assessed before and after completing a 24-week weight loss program. The data values represent the change in brain activity associated with high-calorie foods, the change in brain activity associated with low-calorie foods, and the difference, HC − LC, for each of the eight subjects. If the weight loss program is effective, then a greater change for the HC treatment would be anticipated, on average, compared to the change for the LC treatment. For purposes of this exercise, you can assume that these eight adults are representative of adult Americans.

Subject ID 1 2 3 4 5 6 7 8
HC 4.3 2.1 4.4 2.4 1.4 2.1 2.0 2.9
LC −5.8 −3.1 −2.0 0.4 0.5 1.3 −2.8 −0.3
Difference 10.1 5.2 6.4 2 0.9 0.8 4.8 3.2

Use the Shiny app "Bootstrap Confidence Interval for the Difference in Two Population Means Using Paired Samples" with a minimum of 1,000 samples to construct a 95% bootstrap confidence interval to estimate the mean difference in change in brain activity, HC − LC. (Use

?_d = ?_HC − ?_LC.

Round your answers to three decimal places.)

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