Answer
Confidence interval: $-10.66\lt µ_{men}-µ_{women}\lt-1.34$
We are 95% confident that the difference between the mean step pulse of men and the mean step pulse of women is between -10.66 and -1.34 beats per minute.
Work Step by Step
$n=51$ (use the smaller value of $n$), so:
$d.f.=n-1=50$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$t_{\frac{α}{2}}=t_{0.025}=2.009$
(According to Table VI, for d.f. = 50 and area in right tail = 0.025)
$Lower~bound=(x ̅_1-x ̅_2)-t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(112.3-118.3)-2.009\sqrt {\frac{11.3^2}{51}+\frac{14.2^2}{70}}=-10.66$
$Upper~bound=(x ̅_1-x ̅_2)+t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(112.3-118.3)+2.009\sqrt {\frac{11.3^2}{51}+\frac{14.2^2}{70}}=-1.34$
