Ultrasound is one of many experimental treatments used for soft tissue injuries.
ID: 3360878 • Letter: U
Question
Ultrasound is one of many experimental treatments used for soft tissue injuries. In an experiment to gauge the efficacy of this treatment for knee injuries, seven su bjects with recent knee injuries were enrolled in a trial. The range of motion (in degrees) of the joint was measured first. After a prescribed ultrasound treatment, the range of motion was measured again. Table 1 below contains the pre and post treatment responses from each of these subjects. Table 1: Kncc extensions (dogrees) beforc and after ultrasound 49.2 45.8 Pre 28.2 40.1 42.4 24.7 63.4 48.4 45.2 51.7 60,3 58.0 52.7 Diff A) In the table above, enter the differences (computed Pre - Post) in the empty cells. B) Based on the sample, the average difference in the pre and post treatment responses is C The margin of error for a 90% confidence interval for the true average difference in nee extension before versus after ultrasound treatment is 10.80. Determine the lo Lower Limit: Upper Limit: D) Based on the results of this study, at = 0.1 we can conclude that :--Select- (2 decimal places) er and upper limits for the conf dence interval. (2 decimal places) (2 decimal places)Explanation / Answer
a.
-2.8 -10.7 -11.9 -35.6 5.4 2.4 -4.3
b.
d = ( di/n ) =-57.5/7=-8.21
c.
Confidence Interval
CI = d ± t a/2 * (Sd/ Sqrt(n))
Where,
d = di/n
Sd = Sqrt( di^2 – ( di )^2 / n ] / ( n-1 ) )
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
d = ( di/n ) =-57.5/7=-8.21
Pooled Sd( Sd )= Sqrt [ 1584.71- (-57.5^2/7 ] / 6 = 13.62
Confidence Interval = [ -8.21 ± t a/2 ( 9.63/ Sqrt ( 7) ) ]
= [ -8.21 - 1.943 * (5.15) , -8.21 + 1.943 * (5.15) ]
= [ -18.21 , 1.79 ]
d.
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interpretations:
1. we are 90% sure that the interval [-18.21 , 1.79] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
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