Question

Math & Music (Raw Data, Software Required):
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	586	535
3	604	553
4	573	537
5	516	480
6	554	513
7	546	495
8	607	556
9		554
10		493
11		557

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 (μ₁ − μ₂ > 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. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(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.

Answer 1

Summary statistics:
Variable	Observations	Obs. with missing data	Obs. without missing data	Minimum	Maximum	Mean	Std. deviation
Math SAT Scores (x1)	8	0	8	516.000	607.000	563.375	35.026
Math SAT Scores (x2)	11	0	11	480.000	557.000	523.000	31.509
t-test for two independent samples / Upper-tailed test:
95% confidence interval on the difference between the means:
[ 13.698,	+Inf [
Difference	40.375
t (Observed value)	2.633
t (Critical value)	1.740
DF	17
p-value (one-tailed)	0.009
alpha	0.05
Test interpretation:
H0: The difference between the means is equal to 0.
Ha: The difference between the means is greater than 0.
As the computed p-value is lower than the significance level alpha=0.05, one should reject the null hypothesis H0, and accept the alternative hypothesis Ha.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a right-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =2.63

(d) What is the conclusion regarding the null hypothesis?

reject H₀

_(e) We have proven that students who study music in high school have a higher average Math SAT score than those who do not.