Math & Music: There is a lot of interest in the relationship between studying mu
ID: 3181693 • Letter: M
Question
Math & Music: 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 (x1) Math SAT Scores (x2)
1 521 480
2 571 535
3 604 553
4 588 537
5 531 480
6 559 513
7 531 495
8 602 556
9 554
10 493
11 557
x 563.38 523.00
s2 1102.55 992.80
s 33.20 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 right-tailed test.
This is a left-tailed test.
This is a two-tailed test.
(b) Use software to calculate the test statistic or use the formula
t =
(x1 x2)
s12
n1
+
s22
n2
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 H0
fail to reject H0
(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.
Explanation / Answer
(a) Thsi is right tailed test.
(b)
SE = sqrt(S1^2/n1 + s2^2/n2)
SE = sqrt(1212.47/11 + 965.41/8) = 15.1954
t = ((x1bar - x2bar)-0)/SE
t = 2.4297
degrees of freedom = 16
(c)
p-value = 0.0136
(d)
As p-value is greater than the significance level, we fail to reject the null hypothesis.
reject H0
(e)
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.
X1 X2 Mean 555.5455 518.6250 Variance 1212.4727 965.4107 Observations 11 8 Hypothesized Mean Difference 0 df 16 t Stat 2.4297 P(T<=t) one-tail 0.0136 t Critical one-tail 2.5835