The following questions all refer to Table 1, below. a). Assume Table 1 is set u
ID: 2934525 • Letter: T
Question
The following questions all refer to Table 1, below.
a). Assume Table 1 is set up in the standard way. Which variable is hypothesized to be dependent/response and which is hypothesized to be independent/explanatory? Does this implied relationship seem sensible to you?
b). Find the row percents for the first row
c). Approximately what row percents should you see in the second row if the Level of Happiness and Maximum Adult Education Achieved are independent?
d). What is a good title for this table?
Table 1
Max Adult Education
Achieved
Level of Happiness
Very Happy
Pretty Happy
Not Too Happy
Total
Less Than High School
183
336
119
High School
239
462
96
Some College
281
509
87
Bachelor’s Degree
459
714
102
Advanced Degree
154
213
31
Total
Max Adult Education
Achieved
Level of Happiness
Very Happy
Pretty Happy
Not Too Happy
Total
Less Than High School
183
336
119
High School
239
462
96
Some College
281
509
87
Bachelor’s Degree
459
714
102
Advanced Degree
154
213
31
Total
Explanation / Answer
Solution:
First of all we have to find row totals and columns totals of the table. Completed table is given as below:
Max Adult Education
Level of Happiness
Achieved
Very Happy
Pretty Happy
Not Too Happy
Total
Less Than High School
183
336
119
638
High School
239
462
96
797
Some College
281
509
87
877
Bachelor’s Degree
459
714
102
1275
Advanced Degree
154
213
31
398
Total
1316
2234
435
3985
a). Assume Table 1 is set up in the standard way. Which variable is hypothesized to be dependent/response and which is hypothesized to be independent/explanatory? Does this implied relationship seem sensible to you?
Answer:
The variable level of happiness is hypothesized to be dependent or response and the variable maximum adult education achieved is hypothesized as the independent or explanatory variable. This implied sensible relationship because as the education increases, the level of happiness also increases (except advanced degree).
b). Find the row percents for the first row
The row percents for the first row are given as below:
Row percent = row observation / row total
Max Adult Education
Level of Happiness
Achieved
Very Happy
Pretty Happy
Not Too Happy
Total
Less Than High School
183/638 = 0.286833856
336 / 638 = 0.526645768
119 / 638 = 0.186520376
1
(Table only shows first row)
c). Approximately what row percents should you see in the second row if the Level of Happiness and Maximum Adult Education Achieved are independent?
If level of happiness and maximum adult education achieved are independent, then
P(Level of happiness and maximum adult education achieved) = P(level of happiness) * P(maximum adult education achieved)
Max Adult Education
Level of Happiness
Achieved
Very Happy
Pretty Happy
Not Too Happy
Total
High School
(797/3985)/(1316/3985) = (797/1316) = 0.299874529
797/2234 = 0.579673777
797/435 = 1.832184
1
(Table only shows second row. Row sum is not equal to 1, indicates that variables are not independent.)
d). What is a good title for this table?
Title for this table would be ‘contingency table for level of education and happiness’.
Max Adult Education
Level of Happiness
Achieved
Very Happy
Pretty Happy
Not Too Happy
Total
Less Than High School
183
336
119
638
High School
239
462
96
797
Some College
281
509
87
877
Bachelor’s Degree
459
714
102
1275
Advanced Degree
154
213
31
398
Total
1316
2234
435
3985
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