You are continueing your research into the physiological mea

You are continueing your research into the physiological measurements of men and women. At your request, a medical research center send you the weights, in pounds, of sixteen randomly selected male patients:

151 154 163 169 175 178 185 188 192 195 204 210 218 220 230 240

And sixteen randomly selected female patients:

133 137 145 147 148 152 153 155 162 162 166 167 168 170 180 183

Find the 99% confidence interval for the difference in weights between males and females given these results

Solution

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=192
Standard deviation( sd1 )=26.7457
Sample Size(n1)=16
Mean(x2)=158
Standard deviation( sd2 )=14.2735
Sample Size(n1)=16
CI = [ ( 192-158) ±t a/2 * Sqrt( 715.33246849/16+203.73280225/16)]
= [ (34) ± t a/2 * Sqrt( 57.44) ]
= [ (34) ± 2.947 * Sqrt( 57.44) ]
= [11.66 , 56.34]