In: Statistics and Probability
Question 3
In a study conducted on 335 primary school students in a small district in Malaysia, students at primary levels 4-6 were asked which goal in terms of good grades, athletic ability or popularity (being popular in school) was most important to them. A two-way table (Table 3.1) separating the students by their educational levels and goals is shown below:
Table 3.1
Primary Level |
||||
Goals Grades Popular Sports Total |
4 |
5 |
6 |
Total |
49 |
50 |
69 |
168 |
|
24 |
36 |
38 |
98 |
|
19 |
22 |
28 |
69 |
|
92 |
108 |
135 |
335 |
Table 3.2
School Area |
||||
Goals Grades Popular Sports Total |
Rural |
Suburban |
Urban |
Total |
57 |
87 |
24 |
168 |
|
50 |
42 |
6 |
98 |
|
42 |
22 |
5 |
69 |
|
149 |
151 |
35 |
335 |
ANSWER::
a)
Goals | 4 | 5 | 6 |
Grades | 53.26% | 46.30% | 51.11% |
Popular | 26.09% | 33.33% | 28.15% |
Sports | 20.65% | 20.37% | 20.74% |
yes, there is much of a variation in goals across the three educational levels
b)
Chi-Square Test of independence | |||||||
Observed Frequencies | |||||||
0 | |||||||
0 | rural | suburban | urban | Total | |||
Grades | 57 | 87 | 24 | 168 | |||
Popular | 50 | 42 | 6 | 98 | |||
Sports | 42 | 22 | 5 | 69 | |||
Total | 149 | 151 | 35 | 335 | |||
Expected frequency of a cell = sum of row*sum of column / total sum | |||||||
Expected Frequencies | |||||||
rural | suburban | urban | Total | ||||
Grades | 149*168/335=74.722 | 151*168/335=75.725 | 35*168/335=17.552 | 168 | |||
Popular | 149*98/335=43.588 | 151*98/335=44.173 | 35*98/335=10.239 | 98 | |||
Sports | 149*69/335=30.69 | 151*69/335=31.101 | 35*69/335=7.209 | 69 | |||
Total | 149 | 151 | 35 | 335 | |||
(fo-fe)^2/fe | |||||||
Grades | 4.2033 | 1.6787 | 2.369 | ||||
Popular | 0.9432 | 0.1069 | 1.755 | ||||
Sports | 4.1684 | 2.6634 | 0.6769 |
Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =
18.564
Level of Significance = 0.05
Number of Rows = 3
Number of Columns = 3
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 3- 1 )
= 4
p-Value = 0.0010 [Excel
function: =CHISQ.DIST.RT(χ²,df) ]
Decision: p-value < α , Reject Ho
there is an association between school area and the students' goals of getting good grades, athletic ability or popularity as most important to them.
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