The analyzed data provides evidence that the variables "Politics" and "Sex" are likely not independent.
How to solve
a) Conditional Distribution for Females:
Political View Female Percentage
Conservative 25 41.7%
Moderate 30 50.0%
Liberal 45 75.0%
Total 100 166.7%
b) Conditional Distribution for Males:
Political View Male Percentage
Conservative 20 40.0%
Moderate 35 70.0%
Liberal 25 50.0%
Total 80 160.0%
c) Graphical Comparison:
[See below]
d) Independence of Variables:
Based on the calculated conditional distributions and the graphical comparison, the variables "Politics" and "Sex" appear to be dependent.
The conditional distributions show significant differences in the proportions of females and males holding various political views.
For example, while 75% of females are liberal, only 50% of males identify with the same view.
Similarly, 50% of females are moderate compared to 70% of males.
These disparities suggest that political views and sex are not independent; knowing a student's sex influences the probability of predicting their political affiliation.
Conclusion:
The analyzed data provides evidence that the variables "Politics" and "Sex" are likely not independent. The observed differences in the distributions suggest a possible association between sex and political views in this group of Intro Stats students.
The Complete Question
Politics revisited Look again at the table of political views for the Intro Stats students in Exercise 28. a) Find the conditional distributions (percentages) of political views for the females. b) Find the conditional distributions (percentages) of political views for the males. c) Make a graphical display that compares the two distributions. d) Do the variables Politics and Sex appear to be indepen dent? Explain
Consider a hypothetical dataset for Intro Stats students categorized by political views (Conservative, Moderate, Liberal) and gender (Male, Female):
Gender Political Views Count
Female Conservative 25
Female Moderate 30
Female Liberal 45
Male Conservative 20
Male Moderate 35
Male Liberal 25