4. (8 points) Listed below are the weights (in pounds) of sixteen randomly selec

Question

4. (8 points) Listed below are the weights (in pounds) of sixteen randomly selected athletes before and after a three-month regimen of diet, aerobic exercise and weight training designed to reduce body fat and increase muscle mass. At the 95% confidence level, conduct the formal Si Test for matched pairs differences to test the claim that the weights of the athletes were increased by the training regimen. Weight Weight Before After Regimen Regimen ounds unds 160 161 164 165 169 172 175 176 176 180 186 183 190 186 180 190 192. 194 199 195 203 210 204 214 218 225 228 228 220

Explanation / Answer

4.

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 ) =-28/16=-1.75
Pooled Sd( Sd )= Sqrt [ 402- (-28^2/16 ] / 15 = 4.851
Confidence Interval = [ -1.75 ± t a/2 ( 2.801/ Sqrt ( 16) ) ]
= [ -1.75 - 2.131 * (1.213) , -1.75 + 2.131 * (1.213) ]
= [ -4.334 , 0.834 ]

X Y X-Y (X-Y)^2 155 160 -5 25 161 164 -3 9 165 169 -4 16 172 170 2 4 172 175 -3 9 176 176 0 0 180 186 -6 36 183 190 -7 49 186 180 6 36 190 192 -2 4 194 199 -5 25 195 203 -8 64 210 204 6 36 214 218 -4 16 225 228 -3 9 228 220 8 64 -28 402

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