Answer
Confidence interval: $38.08\lt µ_1-µ_2\lt44.72$
We are 90% confident that the mean difference in cooling time for clear glass versus aluminum is between 38.08 and 44.72 minutes.
Work Step by Step
$n=35$ (use the smaller value of $n$), so:
$d.f.=n-1=34$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.90=1-α$
$α=0.10$
$t_{\frac{α}{2}}=t_{0.05}=1.691$
(According to Table VI, for d.f. = 34 and area in right tail = 0.05)
$Lower~bound=(x ̅_1-x ̅_2)-t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(133.8-92.4)-1.691\sqrt {\frac{9.9^2}{42}+\frac{7.3^2}{35}}=38.08$
$Upper~bound=(x ̅_1-x ̅_2)+t_{\frac{α}{2}}\sqrt {\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=(133.8-92.4)+1.691\sqrt {\frac{9.9^2}{42}+\frac{7.3^2}{35}}=44.72$
