Math :1 Music (Raw Data, software Required): There is a iot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this reiationship. Belnw are the Math SAT scores from a students who studied music through high schooi 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 ciaim at the oos signicance level. Studied Music Nu Music count Math SAT Scores (x1) Math SAT Scores (x2) 1 521 460 2 571 535 3 599 553 4 583 537 5 521 480 6 559 513 7 545 495 s 602 556 9 554 10 493 11 557 You shouid be able copy and paste the data directly into your software program. (a) The claim is that the difference in population means is positive [pl 7 p2 > 0)- what type of test is this? O This is a rightrtailed test. 0 This is e twosteiied test. This is a left-tailed test. X (in) use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances. Rnurld your answer to 2 decimal places. S (c) use software to get the psvalue of the test statistic. Rnund to a decimal places. (d) what is the conclusion regarding the null hypothesis? reject Hu fail to reject Ha I (e) choose the appropriate concluding statement. 0 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. 0 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. 0 We reject the ciaim that students who study music in high school have a higher average Math SAT score than those who do not, 0 we have Emven that students whn stud! music in high school have a higher average Mah SAT amra than thnse who :15 not