Let X and Y equal respectively the blood volumes in millilit

Let X and Y equal, respectively, the blood volumes in milliliters for a male who is a paraplegic and participates in vigorous physical activities and for a male who is able-bodied and participates in everyday, ordinary activities. Assume that X is N(Mux, sigma^2x) and Y is N( Muy,sigmay^2). Following are n = 7 observations of X : 1612, 1352, 1456, 1222, 1560, 1456, 1924. Following are m =10 observations of Y : 1082, 1300, 1092, 1040, 910, 1248, 1092, 1040, 1092, 1288. Using point estimates for Mux and Muy, find a 95% confidence interval for Mux-Muy

Solution

X: n1=7, xbar1=1511.714, s1=222.8675

Y: n2=10, xbar2=1118.4, s2=123.6835

The degree of freedom =n1+n2-2=7+10-2=15

Given a=1-0.95=0.05, t(0.025, df=15) =2.13 (from student t table)

So the lower bound is

(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)

=(1511.714-1118.4) -2.13*sqrt(222.8675^2/7+123.6835^2/10)

=195.4937

So the upper bound is

(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)

=(1511.714-1118.4) +2.13*sqrt(222.8675^2/7+123.6835^2/10)

=591.1343