Answer:
Confidence interval: (1.95,4.45)
Step-by-step explanation:
We are given the following information:
U.S Scores
[tex]\bar{x}_1 = 20.6, s_1 = 5.8, n_1 = 185[/tex]
Mexico Scores
[tex]\bar{x}_2 = 17.4, s_2 = 5.8, n_2 = 86[/tex]
Formula:
Degree of freedom = [tex]n_1 + n_2 -2 = 185 + 86 -2 = 269[/tex]
Confidence interval:
[tex](\bar{x}_1 - \bar{x}_2) \pm t_{critical}\bigg(\sqrt{\displaystyle\frac{s_1^2}{n_1} + \displaystyle\frac{s_2^2}{n_2}}\bigg)[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at}~\alpha_{0.10}\text{ and degree of freedom 269} = \pm1.6505[/tex]
[tex](20.6-17.4) \pm 1.6505\bigg(\sqrt{\displaystyle\frac{33.64}{185} + \displaystyle\frac{33.64}{86}}\bigg)= 3.2 \pm 1.25 = (1.95,4.45)[/tex]
