Question

An adviser is testing out a new online learning module for a placement test. They wish to test the claim that on average the new online learning module increased placement scores at a significance level of α = 0.05. For the context of this problem, μ_D=μ_new–μ_old where the first data set represents the new test scores and the second data set represents old test scores. Assume the population is normally distributed.

H₀: μ_D = 0

H₁: μ_D < 0

You obtain the following paired sample of 19 students that took the placement test before and after the learning module:

New LM	Old LM
57.1	55.8
58.3	51.7
83.6	76.6
50.5	47.5
51.5	48.6
20.6	15.5
35.2	29.9
46.7	54
23.5	21
48.8	58.5
53.1	42.6
76.6	61.2
29.6	26.3
14.5	11.4
43.7	56.3
57	46.1
66.1	72.9
38.1	43.2
44.4	51.1

Find the p-value. Round answer to 4 decimal places.

p-value =   

Answer 1