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, μD=μnew–μold 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: μD = 0
H1: μD < 0
You obtain the following paired sample of 19 students that took the placement test before and
after the learning module:
New
Old LM
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
, New
Old LM
LM
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
Find the p-value. Round answer to 4 decimal places.
44.4 51.1
p-value = 0.1987
, A manager wants to see if it worth going back for a MBA degree. They randomly
sample 18 managers' salaries before and after undertaking a MBA degree and record their
salaries in thousands of dollars. Assume Salaries are normally distributed. Test the claim that the
MBA degree, on average, increases a manager’s salary. Use a 10% level of significance.
t-Test: Paired Two Sample for Means
Old
New Salary Salary
Mean 61.878 56.999
Variance 177.5551 115.8012
Observations 18 18
Pearson Correlation 0.7464
Hypothesized Mean Difference 0
df 17
t Stat 2.9870
P(T<=t) one-tail 0.0024
t Critical one-tail 1.3334
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, μD=μnew–μold 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: μD = 0
H1: μD < 0
You obtain the following paired sample of 19 students that took the placement test before and
after the learning module:
New
Old LM
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
, New
Old LM
LM
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
Find the p-value. Round answer to 4 decimal places.
44.4 51.1
p-value = 0.1987
, A manager wants to see if it worth going back for a MBA degree. They randomly
sample 18 managers' salaries before and after undertaking a MBA degree and record their
salaries in thousands of dollars. Assume Salaries are normally distributed. Test the claim that the
MBA degree, on average, increases a manager’s salary. Use a 10% level of significance.
t-Test: Paired Two Sample for Means
Old
New Salary Salary
Mean 61.878 56.999
Variance 177.5551 115.8012
Observations 18 18
Pearson Correlation 0.7464
Hypothesized Mean Difference 0
df 17
t Stat 2.9870
P(T<=t) one-tail 0.0024
t Critical one-tail 1.3334
