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 ? = 0.05. For the context of this problem, ?_D=?_new-?_oldwhere 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: ?_D= 0

H₁: ?_D

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

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

p-value =

 

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