Two growth hormones are being considered A random sample of

Two growth hormones are being considered. A random sample of 10 rats was given the first hormone and their average weight gain was x(bar)1=2.3 pounds with a standard deviation s1=0.4. Fort the second hormone, a radome sample of 15 rates had an average weight gain of x(bar)2=1.9 pounds with standard deviation s2=0.2. Assume the weight gains follow a normal distribution. Find a 90% confidence interval for the difference in average weight gain for the two growth hormones.

Solution

The degree of freedom =n1+n2-2=10+15-2 =23

Given a=0.1, t(0.05, df=23) = 1.71 (from student t table)

So 90% confidence interval is

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

--> (2.3-1.9) +/- 1.71*sqrt(0.4^2/10+0.2^2/15)

--> (0.1663695, 0.6336305)