A study in Physical Therapy reports on seven different methods to determine crut
ID: 3289343 • Letter: A
Question
A study in Physical Therapy reports on seven different methods to determine crutch length plus two new techniques using linear regression. One of the regression techniques uses the patient's reported height. The study included 109 individuals. The mean of the self-reported heights was 67.9 inches. The regression equation is given below, where y = crutch length and x = self-reported height. The MSE (se2) was reported to be 0.7. In addition, the standard deviation of the self-reported heights was 7.97 inches. Use this information to find a 99% confidence interval estimate for the mean crutch length for individuals who say they are 75 inches tall. (Give your answers correct to one decimal place.)
y = 0.68x + 4.8
Lower Limit _______ Upper Limit _______Explanation / Answer
n = 109
x bar = 67.9
MSE = 0.7
Sx = 7.97
x = 75
Need to find 99% confidence interval estimate for mean crutch length
.
Y^ = 0.68 * 75 + 4.8
Y^ = 55.8
.
The formula of Confidence limit is :
LCL = y^ - t*MSE*sqrt(1/n + s^2)
LCL = 55.8 - 2.622 * 0.7 * sqrt(1/109 + 7.97^2)
LCL = 41.1708
.
UCL =y^ + t*MSE*sqrt(1/n + s^2)
UCL = 55.8 + 2.622 * 0.7 * sqrt(1/109 + 7.97^2)
UCL = 70.4292
.
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