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	526	480
2	581	535
3	589	553
4	583	537
5	531	480
6	554	513
7	541	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 two-tailed test.This is a right-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

	Studied Music ( X )	Σ ( Xi- X̅ )2	No Music ( Y )	Σ ( Yi- Y̅ )2
	526	1444	480	1849
	581	289	535	144
	589	625	553	900
	583	361	537	196
	531	1089	480	1849
	554	100	513	100
	541	529	495	784
	607	1849	556	1089
			554	961
			493	900
			557	1156
Total	4512	6286	5753	9928

Mean X̅ = Σ Xi / n
X̅ = 4512 / 8 = 564
Sample Standard deviation S_X = √ ( (Xi - X̅ )2 / n - 1 )
S_X = √ ( 6286 / 8 -1 ) = 29.9666

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

.This is a right-tailed test.

To Test :-

H0 :- μ₁ − μ₂ = 0

H1 :- μ₁ − μ₂ > 0

Test Statistic :-


t = 2.88

Test Criteria :-
Reject null hypothesis if t > t(α, DF)


DF = 15
t(α, DF) = t( 0.05 , 15 ) = 1.753
t > t(α, DF) = 2.8812 > 1.753
Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 2.8812 ) = 0.0057
Reject null hypothesis if P value < α level of significance
P - value = 0.0057 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Part d)

reject H₀

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.