Question

consider the data of pretest and post test scores

X_{1 (pre)} X_2(post)

2 5

3 7

6 11

5 9

perform a related-samples t-test on above data. a) Conducting a two tailed hypothesis test at the alpha = 0.01 what is the critical t value?

   b) what is the obtained t value that you calculated from the above dataset?

   c) given the obtained t and critical t values, is the mean of the difference scores statistically significant why or why not?

Answer 1

Pre	Post	Difference
2	5	-3
3	7	-4
6	11	-5
5	9	-4
	Total	-16

The null and alternative hypothesis is

a)

Level of significance = 0.01

Sample size = n = 4

Degrees of freedom = n - 1 = 4 - 1 = 3

Critical value = 5.841

( From t table)

b)

Test statistic is

Sample mean of difference = = - 4

Sample standard deviation of difference = = 0.8165

c)

Test statistic | t | > critical value we reject the null hypothesis.

Conclusion: the mean of the difference scores statistically significant.