Question

4.. (10 points). You may assume these data are normal, so apply the appropriate parametric test. An educational researcher has a group of ten students. They take a standardized college-admissions test, then use an online tutorial to help with test taking, vocabulary, and math review. They take the test a second time. Is the difference between their "after" test-prep scores and their "before" test-prep scores significantly greater than 0? (in other words: did the test prep improve their scores?) Before After

Answer 1

H0: Null Hypothesis: (The test preparation did not improve their score)

Hd < 0

HA: Alternative Hypothesis: (The test preparation improved their score) (Claim)

ud > 0

From the given data, values of d = After - Before are got as follows:

2, 1, 4, -2, 1, 0, 8, 2, 1, 4, - 3, 3

From d values, the following statistics are calculated:

n = 12

$\bar{d}$ = 21/12 = 1.75

s_d = 2.8959

SE = s_d/$\sqrt{n}$

= 2.8959/$\sqrt{12}$

0.8360

Test Statistic is given by:

t = 1.75/0.8360

= 2.0933

ndf = 12 - 1 = 11

Take $\alpha$ = 0.05

From Table, critical values of t = $\pm$ 2.2010

Since calculated value of t = 2.0933 is less than critical value of t = 2.2010, the difference is not significant. Fail to reject null hypothesis.

Conclusion: The data do not support the claim that the test preparation improved their score.
The data do not support the claim that