two instructors teach a math course and give an exam over the same material. the
ID: 3220207 • Letter: T
Question
two instructors teach a math course and give an exam over the same material. the grades for the exams are listed in the hypothetical data sets. assume that the student in each class are a random sample from the population of all students who might take the math course.
a) is the difference between the mean scores for each instructor statistically significant? perform a test of significance at level a (alpha)=0.5 based on satterthwaite's approximation (without assuming equality of population standard deviation) carefully show all steps of the test.
b) a test taker passes the exam if they score 60 or more. is the difference between the proportions of test takers who would pass each instructors exam? perform a test significance ( same as part a))
data for the problem:
prof a: prof b:
90. 38
75. 57
76. 51
67. 41
61. 42
69. 46
78. 67
61. 58
55. 66
63. 70
63. 65
72. 84
74. 68
63. 93
73. 93
61. 77
60. 57
52. 49
79
48
60
72
61
77
63
67
83
63
74
80
68
57
Explanation / Answer
a) H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Using separate variance t-test
t=(X1-X2) -(µ1-µ2)/(S1^2/n1+S2^2/n2)
=(67.66-62.33)/(9.49^2/32+16.82^2/18)
=1.24
With 48 degrees of freedom at alpha 0.025 (0.05/2), we get the tCRIT to be 2.0106. Here 1.24 is smaller than 2.0106 and hence we cannot reject H0 stating that there is no difference between mean scores for each instructor.
b) H0: 1 - 2 <= 60 i.e. (1 = 2)
H1: 1 - 2 > 60 i.e. (1 2)
Using separate variance t-test
t=(X1-X2) -(µ1-µ2)/(S1^2/n1+S2^2/n2)
=(67.66-62.33)-60/(9.49^2/32+16.82^2/18)
=-12.71
With 48 degrees of freedom at alpha 0.025 (0.05/2), we get the tCRIT to be 2.0106. Here -12.71 is smaller than -2.0106 and hence we should reject null hypothesis.
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