There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Here are the Math SAT scores from 7 students who studied music through high school and 11 students who did not. The degrees of freedom (d.f.) is given to save calculation time if you are not using software.

	Math SAT Scores											mean	$s^2$	$s$
Music ($x_1$)	525	607	589	581	528	579	567					568	950.333333333333	30.8274769213008
No Music ($x_2$)	481	517	513	503	511	468	519	469	509	536	536	505.636363636364	561.854545454541	23.703471168893
degrees of freedom: d.f. = 10

Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Use a 0.01 significance level.

(a) Find the test statistic.

(b) Find the critical value.

(c) Is there sufficient data to support the claim?
Yes
No