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< 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 =