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.

The 8 students who studied music in high school (x₁)

Math SAT Scores (x1)	x1	s12	s1
532    585    576    630    556    555   585    634	581.6	1280.8	35.79

The 11 students who did not study music in high school (x₂)

Math SAT Scores (x2)	x2	s22	s2
480    535    553    537    480    513   495    556   554   493   557	523.0	992.8	31.51

If you are using software, you should be able copy and paste the data.

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

t =

(c) Use software to calculate the degrees of freedom (d.f.) or use the formula

Round your answer to the nearest whole number.
d.f. =   

(d) What is the critical value of t? Use the answer found in the t-table or round to 3 decimal places.
t_α =  

Answer 1

(b) Use software to calculate the test statistic.

Test statistic = t = 3.7051

(c) Use software to calculate the degrees of freedom (d.f.)

d.f. = 14

d) What is the critical value of t?

tα = 1.761

(by using t-table)

The required output for the two sample t test for the difference between two population means by assuming unequal population variances is given as below:

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	8
Sample Mean	581.625
Sample Standard Deviation	35.7888
Population 2 Sample
Sample Size	11
Sample Mean	523
Sample Standard Deviation	31.5087
Intermediate Calculations
Numerator of Degrees of Freedom	62679.8573
Denominator of Degrees of Freedom	4476.5286
Total Degrees of Freedom	14.0019
Degrees of Freedom	14
Standard Error	15.8228
Difference in Sample Means	58.6250
Separate-Variance t Test Statistic	3.7051
Upper-Tail Test
Upper Critical Value	1.7613
p-Value	0.0012
Reject the null hypothesis