For questions 5 - 9 below, use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.

Five students took a math test before and after tutoring. Their scores were as follows.

Student	A	B	C	D	E
Before	71	66	67	77	75
After	75	75	65	80	87

Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

5. State the null and alternative hypotheses.

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6. Find d, d bar, and s_d,

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7. Find the value of the test statistic, t.

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8. Find the critical value(s) and state the decision about the null hypothesis.

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9. State the conclusion in non-technical terms.

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