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. 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	555		594.666666666667	1221.25	34.9463875100131
No Music (x2)	511	509	544	524	533	565	531	585	571	533	540.6	651.155555555545	25.5177498137188
degrees of freedom: d.f. = 15

Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Use a 0.01 significance level.

(a) Find the test statistic.

(b) Find the critical value.

(c) Is there sufficient data to support the claim?
Yes
No

Answer 1

Let be the the average Math SAT scores of high school students who study music.

Let be the the average Math SAT scores of high school students who do not study music..

Given:

For: =594.667, s₁ = 34.9464, n₁ = 9

For: = 540.6, s₂ = 25.5177, n₂ = 10

Since we are considering unequal variances, we calculate the degrees of freedom as given below.

Therefore df Rounded = 15

The Hypothesis:

H0: = : The average Math SAT scores of high school students who study music is equal to the average Math SAT scores of high school students who do not study music..

Ha: > : : The average Math SAT scores of high school students who study music is greater than the average Math SAT scores of high school students who do not study music.

This is a Right tailed test.

(a) The Test Statistic:

The p Value:    The p value (Right Tail) for t = 3.82, df = 15 is; p value = 0.9992

(b) The Critical Value:   The critical value (Right Tail) at = 0.01, df = 15, tcritical = +2.947

The Decision Rule:   If tobserved is > tcritical, Then Reject H0.

Also If the P value is < α, Then Reject H0

The Decision:    Since t observed (3.82) is > tcritical (2.947), We Reject H0.

Also since P value (0.0008) is < (0.01), We Reject H0.

(c) The Conclusion: YES, There is sufficient evidence at the 99% significance level to conclude that the average Math SAT scores of high school students who study music is greater than the average Math SAT scores of high school students who do not study music.