5. There is a lot of interest in the relationship between studying music and stu

Question

5. There is a lot of interest in the relationship between studying music and studying math. We will investigate this by looking at the Math SAT scores from 8 students who studied music through high school and 11 students who did not. The statistics are given in the table below. 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. Music8 591.6 37.08 No Music523.031.51 (a) (1 point) What hypothesis test should you use for this problem? Circle your answer Mean-1 Sample Mean-2 Samples, Dependent Mean-2 Samples, Independent Proportion-2 Samples Proportion-1 Sample (b) (1 point) What calculator function will you use? (c) (2 points) Determine the null and alternative hypotheses: ?? Hi: P-value: (d) (2 points) Perform the hypothesis test. Conclusion: (e) (2 points) Find and interpret the 99% confidence interval.

Explanation / Answer

a)

mean 2 samples

c)

H0 : mu1 = mu2
H1 : mu1 > mu2

d)

t = (mu1 - mu2)/sqrt(s1^2/n1 + s2^2/n2)
= ( 591.6 - 523)/sqrt(37.08^2/8+ 31.51^2/11)
= 4.2371

p value = .0019

Reject the null hypothesis

e)

t value at 99% = 3.707

CI = (mu1 - mu2) +/- sqrt(s1^2/n1 + s2^2/n2)
= ( 591.6 - 523) +/- 3.707 * sqrt(37.08^2/8+ 31.51^2/11)
= (8.5824,128.6176)

The 99% CI is (8.5824,128.6176)

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