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	516	480
2	586	535
3	594	553
4	588	537
5	526	480
6	554	513
7	531	495
8	597	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 two-tailed test.    This is a left-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 H₀fail 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

Mean X̅1 = Σ Xi / n
X̅ = 4492 / 8 = 561.5
Sample Standard deviation SX1 = √ ( (Xi - X̅ )2 / n - 1 )
SX1 = √ ( 7936 / 8 -1 ) = 33.6707

Mean X̅2 = ΣYi / n
Y̅ = 5753 / 11 = 523
Sample Standard deviation SX2 = √ ( (Yi - Y̅ )2 / n - 1 )
SX2 = √ ( 9928 / 11 -1) = 31.5087

Part a)

This is a right-tailed test.

Part b)

Test Statistic :-


t = 2.53

Part c)

DF = 14

P - value = P ( t > 2.5278 ) = 0.0121

Part d)

Reject null hypothesis if P value < α level of significance
P - value = 0.0121 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Part e)

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.