3. The objectives of a study by Kennedy and Bhambhani (1991) were to use physiol

Question

3. The objectives of a study by Kennedy and Bhambhani (1991) were to use physiological measurements to determine the test-retest reliability of the Baltimore Therapeutic Equipment Work Simulator during three simulated tasks performed at light, median, and heavy work intensities, and to examine the criterion validity of these tasks by comparing them to real tasks performed in a controlled laboratory setting. Subjects were 30 healthy men between the ages of 18 and 35. The investigators reported a standard deviation of 0.57 for variable peak oxygen consumption (l/min) during one of the procedures Assuming normality, compute a 95% confidence interval for the population standard deviation for the oxygen consumption variable.

Explanation / Answer

ci = (n-1) s^2 / ^2 right < ^2 < (n-1) s^2 / ^2 left
where,
s = standard deviation
^2 right = (1 - confidence level)/2
^2 left = 1 - ^2 right
n = sample size
since alpha =0.05
^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
^2 left = 1 - ^2 right = 1 - 0.025 = 0.975
the two critical values ^2 left, ^2 right at 29 df are 45.7223 , 16.047
s.d( s^2 )=0.57
sample size(n)=30
confidence interval for ^2= [ 29 * 0.3249/45.7223 < ^2 < 29 * 0.3249/16.047 ]
= [ 9.4221/45.7223 < ^2 < 9.4221/16.0471 ]
[ 0.2061 < ^2 < 0.5872 ]
and confidence interval for = sqrt(lower) < < sqrt(upper)
= [ sqrt (0.2061) < < sqrt(0.5872), ]
= [ 0.454 < < 0.7663 ]

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