Question

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 level.

	Studied Music	No Music
count	Math SAT Scores (x1)	Math SAT Scores (x2)
1	516	480
2	571	535
3	594	553
4	578	537
5	521	480
6	564	513
7	541	495
8	607	556
9		554
10		493
11		557
x	561.50	523.00
s2	1089.43	992.80
s	33.01	31.51

If you are using software, 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 left-tailed test.

This is a two-tailed test.  

  This is a right-tailed test.

(b) Use software to calculate the test statistic or use the formulat =  

(x1 − x2) − δ

s12 n1 + s22 n2

where δ is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.

t =

To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(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

	x	y
	516	480
	571	535
	594	553
	578	537
	521	480
	564	513
	541	495
	607	556
		554
		493
		557
COUNT	8	11
	0.1250	0.0909
	0.2159
TOTAL	4492.0000	5753.0000
MEAN	561.5000	523.0000
VARIANCE	953.2500	902.5455
	7626.0000
	9928.0000
	17554.0000
	1032.5882
	222.9452
	14.9313

(a) we frame the Hypothesis

Since : So, it's the One Tailed ( Right Tailed ) Hypothesis Test.

(b)

= 17554

To test the we use the t - Statistic

(c) & (d)

p - value:

Case (i)

The p-value is 0.0097 at = 0.01

· If the p-value ≤ α, we reject the null hypothesis in favour of the alternative hypothesis.

If the p-value > α, we fail to reject the null hypothesis. We do not have enough evidence to support the alternative hypothesis

Since p - value < i.e 0.0097 < 0.01; So, We Reject  

Case(ii)

The p-value is .0097 at = 0.05

Since p - value < i.e 0.0097 < 0.05; So, We Reject  

(e) Therefore we Conclude that i.e We cconclue that

Therefore "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".