Question

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H_0: µ_D = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.

Observation	A	B
1	1	3
2	3	4
3	5	7
4	4	4
5	8	9

What is the M_D? (one decimal)

What is the estimated standard deviation of the difference scores? (four decimals)

What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.) (round your answer to this question to four decimals)

What is the t statistic for the repeated-measures t test to test the null hypothesis H₀: µ_D = 0? (two decimals)

Answer 1

M_D =-1.200

estimated standard deviation of the difference scores =0.8367

estimated standard error of the mean difference scores =0.3742

t statistic for the repeated-measures t test =-3.21