6. (10 points) Listed below are the times (in seconds) required by twelve random

Question

6. (10 points) Listed below are the times (in seconds) required by twelve randomly selected subjects to complete a particular skill-related task. The first column is the time required by each subject on the first attempt. The second column is the time required by the subject after 5 minutes of practice. At the 95% confidence level, conduct the formal Wilcoxon Signed-Ranks Test to test the claim that the population of paired differences has a median of zero. Time On Time After 5 Minutes First Attempt Of Practice (Seconds) Seconds 45 42 40 45 38 37 70 68 42 39 55 55 56 59

Explanation / Answer

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 ) =2/12=0.167
Pooled Sd( Sd )= Sqrt [ 122- (2^2/12 ] / 11 = 3.326
Confidence Interval = [ 0.167 ± t a/2 ( 1.92/ Sqrt ( 12) ) ]
= [ 0.167 - 2.201 * (0.96) , 0.167 + 2.201 * (0.96) ]
= [ -1.946 , 2.28 ]

X Y X-Y (X-Y)^2 45 42 3 9 62 60 2 4 40 45 -5 25 38 37 1 1 70 68 2 4 84 88 -4 16 42 39 3 9 55 55 0 0 61 60 1 1 49 45 4 16 56 62 -6 36 60 59 1 1 0 0 0 0 0 0 0 0 2 122

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