Question

Students at the local high school are given the SAT in their freshman year. They are...

Students at the local high school are given the SAT in their freshman year. They are given the same test again as seniors. Their scores on the math section are listed below. It is reasoable to assume that the population variances are equal.

Freshmen Seniors
736 519
681 601
497 421
565 478
557 585
546 409
517 712
697 708
414 664
569 484
612 511
648 429

A:What are the hypotheses if you want to test whether or not high school has helped prepare these students for the SAT?

b What is the value of the test statistic and p-value?
c What are your conclusions at the 5% significance level?
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The statistical software output for this problem is :

Two sample T hypothesis test:
μ1 : Mean of Freshmen
μ2 : Mean of Seniors
μ1 - μ2 : Difference between two means
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 ≠ 0
(with pooled variances)

Hypothesis test results:

Difference Sample Diff. Std. Err. DF T-Stat P-value
μ1 - μ2 43.166667 41.239676 22 1.0467266 0.3066

Test statistics = 1.047

P-value = 0.3066

At 5% significance level fail to reject the null hypothesis .

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