A random sampleof married men all retired, were classified according to theiredu
ID: 2917525 • Letter: A
Question
A random sampleof married men all retired, were classified according to theireducational level and number of children as shown in the tablebelow. The idea is to determine if the size of a family isindependent on the level of education attained by the father.
There two valuesin each cell. The number, not in parenthesis, represents theobserved value: Oij, whereas the numberin parenthesis represents the expected value corresponding to eachobservation, that is, eij. For examplein cell #1, 14 is the observed value whereas 18.7 is the expectedvalue.
Number ofChildren
Education level
0-1
2-3
over 4
Elementary
14
37
32
83
Secondary
19
42
17
78
College
12
17
10
39
45
96
59
200
Perform acontingency analysis on the data to determine if there is anydependency between the number of level of education attained by thefather and the size of his family. Use = 0.05?
H0: ;H1:
Critical Region: =
Test Statistics: =
Degrees of Freedom (DF):=
Decision: Reject/Do not Reject H0
Number ofChildren
Education level
0-1
2-3
over 4
Elementary
14
37
32
83
Secondary
19
42
17
78
College
12
17
10
39
45
96
59
200
Explanation / Answer
How to calculate the expected value in each cell 0-1 2-3 >3 E 45*83/200 96*83/200 59*83/200 S 45*78/200 96*78/200 59*78/200 C 45*39/200 96*39/200 59*39/200
??(observed value - expected value)2 / expectedvalue
for example first cell valueis 14, first cell value expected is 18.675, difference 4.675,square is 21.85
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