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.

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 two-tailed test. This is a left-tailed test.    This is a right-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.

Studied Music No Music count Math SAT Scores (x1) Math SAT Scores (x2) 1 516 480 2 576 535 3 594 553 4 578 537 5 516 480 6 549 513 7 541 495 8 607 556 9 554 10 493 11 557

Explanation / Answer

In excel

a) this is right-tailed test

b) t =2.407256

c) p-value =0.01385

d) reject H0

as p-value < 0.05

e)

a) 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.

is correct

t-Test: Two-Sample Assuming Equal Variances Math SAT Scores (x1) Math SAT Scores (x2) Mean 559.625 523 Variance 1185.410714 992.8 Observations 8 11 Pooled Variance 1072.110294 Hypothesized Mean Difference 0 df 17 t Stat 2.407256876 P(T<=t) one-tail 0.013858232 t Critical one-tail 1.739606726 P(T<=t) two-tail 0.027716464 t Critical two-tail 2.109815578

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