20) Your professor is interested in determining if the time a student spends tak
ID: 3142062 • Letter: 2
Question
20) Your professor is interested in determining if the time a student spends taking an examinations is related to the grade that the student earns on the exam. He has gathered the following information on examination scores and the length of time the student takes to complete it. The values in the table are the number of students in each category. Test to see if there is a relationship (include all steps including a statement of the hypotheses you are testing) use a 5% significance level. What does your conclusion mean?
Grade Time Spent
Less than ½ Hour
½ Hour to 1 Hour
More than one Hour
A
4
6
12
B
2
18
15
C
10
20
17
D
6
8
7
F
5
5
5
Grade Time Spent
Less than ½ Hour
½ Hour to 1 Hour
More than one Hour
A
4
6
12
B
2
18
15
C
10
20
17
D
6
8
7
F
5
5
5
Explanation / Answer
20)
Set
H0 : There is no relation between the time a student spends in taking the examination and the grade he earned.
H1 : There is relation between the time a student spends in taking the examination and the grade he earned.
Degrees of freedom = (r-1)(c-1) = (5-1)(3-1) = 8
Chi square = Sum[ (O-E)2/ E]
= 9.98
Table value of chi- square at alpha =0.05 = 15.5
calculated value of chi-square < table value.
Therefore H0 is accepted.
There is no relation between the time a student spends in taking the examination and the grade he earned.
Grade Time spent Less than 1/2 hour 1/2 - 1 hour more than 1 hour Total A 4 6 12 22 B 2 18 15 35 C 10 20 17 47 D 6 8 7 21 E 5 5 5 15 TOTAL 27 57 56 140
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