Question

Let’s say I want to see if four years of college can improve SAT scores. 5 randomly sampled high school freshman were asked to take the SAT and their scores were (1010, 1150, 1310, 1250, 980). After four years of college those same 5 students again took the SAT exam. Their scores after college were (1030, 1100, 1380, 1240, 1100). State the null and alternative hypotheses, find the test statistic, the rejection region, the p-value and state your conclusion.

Answer 1

Scores in first year

Since we know that

Since we know that

scores 4 years later

Since we know that

Since we know that

Now, we will test the hypothesis for the difference

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:
If population variance are equal(If nothing is written about equality of population variance, most of the time they are equal)

Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are
n1 + n2 - 2 = 5 + 5 - 2 = 8
This implies that



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