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. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

	Studied Music	No Music
count	Math SAT Scores ( x 1 )	Math SAT Scores ( x 2 )
1	531	480
2	576	535
3	599	553
4	578	537
5	516	480
6	549	513
7	531	495
8	602	556
9		554
10		493
11		557
x	560.25	523.00
s 2	1086.21	992.80
s	32.96	31.51

If you are using software, you should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive ( ? ₁ ? ? ₂ > 0). What type of test is this?

____This is a left-tailed test.

____This is a right-tailed test.

____ This is a two-tailed test.

(b) Use software to calculate the test statistic or use the formula t =

( x ₁ ? x ₂ ) ? ?

s 1 2 n 1 + s 2 2 n 2

where ? is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.

t = ____

To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer. (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = ____ (d) What is the conclusion regarding the null hypothesis?

____reject H ₀

_{____} fail to reject H ₀

(e) Choose the appropriate concluding statement.

_____The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

_____There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.

_____ We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

_____We have proven that students who study music in high school have a higher average Math SAT score than those who do not.