Answer
Confidence interval: $-30.75\lt µ_1-µ_2\lt-11.25$
We are 95% confident that $µ_1-µ_2$ is between -30.75 and -11.25.
Work Step by Step
$n=32$ (use the smaller value of $n$), so:
$d.f.=n-1=31$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.040$
(According to Table VI, for d.f. = 31 and area in right tail = 0.025)
$Lower~bound=(x ̅_1-x ̅_2)-t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(94.2-115.2)-2.040\sqrt {\frac{15.9^2}{40}+\frac{23.0^2}{32}}=-30.75$
$Upper~bound=(x ̅_1-x ̅_2)+t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(94.2-115.2)+2.040\sqrt {\frac{15.9^2}{40}+\frac{23.0^2}{32}}=-11.25$
