Question

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Before: 74,83,75,88,84,63,93,84,91,77 After: 73,77,70,77,74,67,95,83,84,75 a. Write the null and the alternative hypothesis? b. are the means independent or dependent? explain. c. is it one or two tailed test? d. find the p value? E. write the decision. F. write the conclusion.

Answer 1

Before	After	Difference
74	73	1
83	77	6
75	70	5
88	77	11
84	74	10
63	67	-4
93	95	-2
84	83	1
91	84	7
77	75	2
	Total	37

Claim: The mean score is not affected by the course.

a) The null and alternative hypothesis is

b) Dependent, because data are given before and after type.

c) Two-tailed test because the alternative hypothesis has not equal to sign.

Level of significance = 0.05

Sample size = n = 10

Sample mean of difference = = 3.7

Sample standard deviation of difference = = 4.9453

Test statistic is

Degrees of freedom = n - 1 = 10 - 1 = 9

d) P-value = 2*P(T > 2.37) = 0.0422

e) P-value < 0.05 we reject null hypothesis.

Conclusion:

f) The mean score is affected by the course.