Question

A standardized statistics test was given to 50 females and 75 males. The females made an
average grade of 76 with a standard deviation of 6, while the males made an average grade
of 82 with a standard deviation of 8. Find a 96% confidence interval for the difference µ1
and µ2
, where µ1
the mean score of all males is and µ2
is the mean score of all females
who took this test.

Answer 1

$96\%CI=(\bar x_1-\bar x_2-t^*s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}},\bar x_1+\bar x_2-t^*s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}})$.

Here $t^*=t_{0.02,n_1+n_2-2}=2.076,$

$s_p=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}=\sqrt{\frac{(75-1)8^2+(50-1)6^2}{75+50-2}}=7.2695.$

So, $96\%CI=(82-76-2.076*7.2695\sqrt{\frac{1}{75}+\frac{1}{50}},82-76+2.076*7.2695\sqrt{\frac{1}{75}+\frac{1}{50}})=$

$=(3.25,8.75).$