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	581	535
3	594	553
4	578	537
5	531	480
6	554	513
7	546	495
8	592	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 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

Using excel Select Data>Data analysis>T-test : two sample assuming unequal variance Excel output as follows t-Test: Two-Sample Assuming Unequal Variances

Variable Variable Mean 561.5 848 523 992.8 8 Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 16 2.748216 0.007143 1.745884 0.014286 2.119905

a) Test hypothesis are Ho: ul-u2 =0 H:ul-u2 >0 Right tailed test b) Test statistic t =2.75 c) df=16 p-value =P(t>2.75)=0.0071 d) Since p-value <0.05 hence reject the null hypothesis e) there si sufficient evidence to conclude that the students who study music in high school have a higher average Math SAT score than those who do not.