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 a positive effect on the math scores.  1. State the null and alternative hypotheses. Solution:    2. Find d, , and sd,.  Note: It doesn’t make any difference which row you subtract Solution:    3. Find the value of the test statistic, t. Solution:    4. Only Find the critical value(s) and state the decision about the null hypothesis using the test statistic and the critical value Solution:    5. State the conclusion in non-technical terms. Solution:
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