For questions 5 -9 below, use the traditional method of hypothesis testing to te

Question

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 Before 71 67 75 75 75 After 65 80 87 Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores. S. State the null and alternative hypothesis 6. find d, d and sa 7. find the value of the test statistic, t. 8. Find the critical value(s) and state the decision about the null hypothesis 9. State the conclusion in non-technical terms. GETmE |ge] -See-Page 100% Print Layout View

Explanation / Answer

5)

ho: There is no significant difference in the mean math score before and after tutoring. U1 = u2

h1: mean math score after tutoring is greater than that of before tutoring. U1 - u2 < 0

6)

diff

-4

-9

2

-3

-12

mean_d -5.2 AVERAGE

sd_d 5.449770637 STDEV

7)

t = mean_d / sd_d/sqrt(n)

=-5.2/(5.449771/SQRT(5))

-2.133585702

8)

t(a,n-1)

=T.INV(0.05,4)

-2.131846786

since -t< -t(a,n-1), I reject ho at 5% level of significance

9)

mean math score after tutoring is greater than that of before tutoring. U1 - u2 < 0

before after diff 71 75 -4 66 75 -9 67 65 2 77 80 -3 75 87 -12

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