There is a lot of interest in the relationship between studying music and studyi

Question

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.

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 (1 2 > 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 or use the formula

where 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 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.

Studied Music No Music count Math SAT Scores (x1) Math SAT Scores (x2) 1 521 480 2 586 535 3 604 553 4 588 537 5 531 480 6 549 513 7 546 495 8 607 556 9 554 10 493 11 557 x 566.50 523.00 s2 1135.14 992.80 s 33.69 31.51 X1 X2 n1

Explanation / Answer

Part a

This is a right tailed test. (Because this is a one tailed test with ‘greater than’ alternative hypothesis)

Part b

The test statistic value by using excel is given as below:

t-Test: Two-Sample Assuming Unequal Variances

Math SAT Scores (x1)

Math SAT Scores (x2)

Mean

566.5

523

Variance

1135.142857

992.8

Observations

8

11

Hypothesized Mean Difference

0

df

15

t Stat

2.855008085

P(T<=t) one-tail

0.006021917

t Critical one-tail

1.753050325

P(T<=t) two-tail

0.012043834

t Critical two-tail

2.131449536

Test statistic = t = 2.86

Part c

P-value = 0.0060 (by using excel)

Part d

We are given = 0.05 and p-value = 0.0060

P-value < , so we reject the null hypothesis 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.

t-Test: Two-Sample Assuming Unequal Variances

Math SAT Scores (x1)

Math SAT Scores (x2)

Mean

566.5

523

Variance

1135.142857

992.8

Observations

8

11

Hypothesized Mean Difference

0

df

15

t Stat

2.855008085

P(T<=t) one-tail

0.006021917

t Critical one-tail

1.753050325

P(T<=t) two-tail

0.012043834

t Critical two-tail

2.131449536

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