What is the upper bound of the percentage of body fat (with 95% confidence) for a person with a girth of 150cm (correct to three decimal places)?
Added by Ryan L.
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Assume the relationship between body fat percentage (Y) and girth (X) is modeled by a simple linear regression: \[ Y = \beta_0 + \beta_1 X + \epsilon \] where \(\epsilon \sim N(0, \sigma^2)\). Show more…
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The BODYFAT dataset was developed using randomly selected patients who were treated by a particular sports injury rehabilitation group. The purpose was to determine if girth (in centimeters) could be used to predict body fat (as a percentage) and to estimate the percentage of body fat (with 99% confidence) of a person who has a girth of 150cm. Girth is easily and accurately evaluated with a tape measure. Body fat percentage is measured via hydrostatic weighing, but this is too expensive and impractical to be easily deployed in most physicians' offices. Please conduct this analysis using a 1% significance level. Girth 99.1 76.0 83.1 88.5 118.0 104.3 79.5 108.8 81.9 76.6 88.7 90.9 89.0 78.0 83.2 85.6 90.3 104.5 95.6 103.1 89.9 104.0 95.3 105.0 83.5 86.7 93.0 76.0 106.1 109.3 104.3 100.5 77.9 101.6 99.7 96.7 95.8 104.8 92.4 95.0 86.0 90.6 105.5 79.4 126.2 98.0 95.5 73.7 86.4 122.1 Fat% 19.0 8.4 9.2 21.8 33.6 31.7 6.4 24.6 4.1 12.8 12.3 8.5 26.0 7.3 13.4 22.3 20.2 16.8 18.4 27.7 17.4 26.4 11.3 27.1 17.2 10.7 18.1 13.7 28.1 23.0 30.8 16.5 7.4 18.2 25.1 16.1 30.2 25.4 25.9 21.6 8.8 19.5 31.0 10.4 33.1 20.2 21.9 11.2 10.9 45.1 What value of alpha (as a proportion and not as a percent) will be used for this analysis? Please run the regression using Minitab. Do not forget to store the standardized residuals or obtain the relevant graph. What value do you get for S (show four decimal places)? Please indicate the value of the test statistic (showing 2 decimal places) that indicates that this regression is useful. Actual body fat percentage typically deviates from the predicted value by _____ percentage points (correct to four decimal points) Girth explains _____ % of the variability in body fat percentage (correct to one decimal place). Increasing girth by one centimeter will increase average body fat percentage by _____ percentage points (correct to four decimal places). A person with a girth of zero (??) centimeters will, on average, have a body fat percentage of _____ (correct to three decimal places). What body fat percentage can a person with a girth of 150cm reasonable expect (correct to three decimal places)? What is the lower bound of the average percentage of body fat (with 95% confidence) for all people who have a girth of 150cm (correct to three decimal places)? What is the upper bound of the percentage of body fat (with 95% confidence) for a person with a girth of 150cm (correct to three decimal places)?
Ameer S.
The BODYFAT dataset was developed using randomly selected patients who were treated by a particular sports injury rehabilitation group. The purpose was to determine if girth (in centimeters) could be used to predict body fat (as a percentage) and to estimate the percentage of body fat (with 99% confidence) of a person who has a girth of 150cm. Girth is easily and accurately evaluated with a tape measure. Body fat percentage is measured via hydrostatic weighing, but this is too expensive and impractical to be easily deployed in most physicians' offices. Please conduct this analysis using a 1% significance level. Girth Fat% 99.1 19 76 8.4 83.1 9.2 88.5 21.8 118 33.6 104.3 31.7 79.5 6.4 108.8 24.6 81.9 4.1 76.6 12.8 88.7 12.3 90.9 8.5 89 26 78 7.3 83.2 13.4 85.6 22.3 90.3 20.2 104.5 16.8 95.6 18.4 103.1 27.7 89.9 17.4 104 26.4 95.3 11.3 105 27.1 83.5 17.2 86.7 10.7 93 18.1 76 13.7 106.1 28.1 109.3 23 104.3 30.8 100.5 16.5 77.9 7.4 101.6 18.2 99.7 25.1 96.7 16.1 95.8 30.2 104.8 25.4 92.4 25.9 95 21.6 86 8.8 90.6 19.5 105.5 31 79.4 10.4 126.2 33.1 98 20.2 95.5 21.9 73.7 11.2 86.4 10.9 122.1 45.1 1) Indicate the value of the test statistic (showing 2 decimal places) that indicates that this regression is useful. 2) Actual body fat percentage typically deviates from the predicted value by _____ percentage points (correct to four decimal points) 3) Girth explains _____ % of the variability in body fat percentage (correct to one decimal place). 4) Increasing girth by one centimeter will increase average body fat percentage by _____ percentage points (correct to four decimal places). 5) A person with a girth of zero (??) centimeters will, on average, have a body fat percentage of _____ (correct to three decimal places).
Body Fat. J. McWhorter et al. of the College of Health Sciences at the University of Nevada, Las Vegas, studied physical therapy students during their graduate school years. The researchers were interested in the fact that, although graduate physical therapy students are taught the principles of fitness, some have difficulty finding the time to implement those principles. In the study, published as "An Evaluation of Physical Fitness Parameters for Graduate Students" (Journal of American College Health, Vol. 51, No. 1, pp. 32-37), a sample of 27 female graduate physical therapy students had a mean of 22.46 percent body fat. a. Assuming that the percent body fat of female graduate physical therapy students is normally distributed with a standard deviation of 4.10 percent body fat, determine a 95% confidence interval for the mean percent body fat of all female graduate physical therapy students. b. Obtain the margin of error, E, for the confidence interval you found in part (a). c. Explain the meaning of E in this context in terms of the accuracy of the estimate. d. Determine the sample size required to have a margin of error of 1.55 percent body fat with a 99% confidence level.
Madhur L.
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