Question

In: Statistics and Probability

Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...

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 (μ1μ2 > 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.

Solutions

Expert Solution

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.


Related Solutions

Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
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...
Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
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...
Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
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...
Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
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...
Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
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...
ath & Music (Raw Data, Software Required): There is a lot of interest in the relationship...
ath & 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...
Math & Music: There is a lot of interest in the relationship between studying music and...
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...
There is a lot of interest in the relationship between studying music and studying math. We...
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. Here are the Math SAT scores from 9 students who studied music through high school and 10 students who did not. The degrees of freedom (d.f.) is given to save calculation time if you are not using software. Math SAT Scores mean ?2s2 ?s Music (x1) 627 625 605 568 567 619 548 638...
There is a lot of interest in the relationship between studying music and studying math. We...
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. Here are the Math SAT scores from 9 students who studied music through high school and 10 students who did not. The degrees of freedom (d.f.) is given to save calculation time if you are not using software. Math SAT Scores mean ?2s2 ?s Music (x1) 627 625 605 568 567 619 548 638...
There is a lot of interest in the relationship between studying music and studying math. We...
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. The 8...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT