The Department of Education would like to determine if there are gender differences in the performance of twins on the state mandated mathematics examination. As a result, they have collected data on twelve sets of twins that are male and female. These are reported in the table below:
|
Female
|
94
|
75
|
95
|
87
|
97
|
86
|
83
|
82
|
87
|
80
|
86
|
78
|
|
Male
|
78
|
95
|
85
|
87
|
92
|
88
|
100
|
84
|
82
|
75
|
86
|
82
|
a. What hypotheses should be used to complete this test?
b. What type of test are you using (Z, t, F, χ2), what is its critical value at α = 0.05?
c. Perform the test and interpret your conclusions.