Discuss the below problem:
Q: The Department of Management Science at Tech has sampled 250 of its majors and compiled the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester.
GPA Frequency
0-0.5 1
0.5-1.0 4
1.0-1.5 20
1.5-2.0 35
2.0-2.5 67
2.5-3.0 58
3.0-3.5 47
3.5-4.0 18
250
The sample mean - for this distribution is 2.5 and the sample standard deviation (s) is X 0.72. Determine if the student GPAs are normally distributed using a .05 level of significance (i.e. a = .05).
| Range |
Observed Frequency (fo) |
Theoretical Frequency (ft) |
(fo - ft)2/ft |
| 0 - 2,000 |
7 |
7.3494 |
0.0166 |
| 2,000 - 3,000 |
22 |
25.5898 |
0.5036 |
| 3,000 - 4,000 |
50 |
54.0996 |
0.3107 |
| 4,000 - 5,000 |
62 |
61.2848 |
0.0083 |
| 5,000 - 6,000 |
40 |
37.2107 |
0.2091 |
| 6,000+ |
19 |
14.4005 |
1.4691 |
| |
|
|
2.5174 |
| |
|
|
|
| Number of Obs. = |
200 |
|
|
| Mean = |
4,200 |
|
|
| Standard Deviation = |
1,232 |
|
|
| |
|
|
|
| Degrees of Freedom = |
3 |
|
|
| |
|
|
|
| Using 5% Level of Significance, the Chi-Square value = |
7.81473 |
| |
|
|
|
| Decision: |
The distribution is normal |
|