In order to see the effect of hours of sleep on tests of different skill categories (vocabulary, reasoning, and arithmetic), tests consisting of 20 questions each in each category were given to 16 students, four each based on the hours of sleep they had on the previous night. Each right answer is given one point. Table gives the cumulative scores of the each of the four students in each category.
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Table
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Hours of sleep
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Category
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Vocabulary
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Reasoning
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Arithmetic
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0
|
44
|
33
|
35
|
|
4
|
54
|
38
|
18
|
|
6
|
48
|
42
|
43
|
|
8
|
55
|
52
|
50
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Test at the 0.05 level whether the true mean performance for different hours of sleep is the same. Also, test at the 0.05 level whether the true mean performance for each category of the test is the same.