# GOV 350K Study Guide - Quiz Guide: Bernoulli Distribution, Binomial Distribution, The Book Of Lost Tales

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Statistical Analysis in Political Science

Homework Assignment No. 3 (Due Thursday, February 27)

I. In 1984, a Gallup Survey asked a national sample of respondents:

Recently there has been a lot of talk about women's rights. Some people feel that women should

have an equal role with men in running business, industry and government. Others feel that

women should not generally have equal leadership roles and that even if they want to work they

should still have primary responsibility for running the home and family. What is your opinion

on this issue?

Even If They Work

Still Responsible

Equal Role For Running Home

1 2 3 4 5 6 7

Responses to this question from men and women are summarized in the following frequency

distributions:

Women Men

Value Frequency Percent Value Frequency Percent

1 274 37.9 1 211 30.2

2 87 12.0 2 93 13.3

3 80 11.1 3 75 10.7

4 112 15.5 4 134 19.2

5 76 10.5 5 88 12.6

6 41 5.7 6 48 6.9

7 53 7.3 7 49 7.0

Total 723 100.0 Total 698 100.0

(1) How would you describe both distributions in terms of their central tendency and variation?

Calculate the most appropriate descriptive statistics. If necessary, consider the scale as a

continuum and use the decimal point in your results.

(2) Compare the two groups' opinion toward women's role.

(3) For men and women in the Gallup sample, which group is more homogeneous in their

opinion toward women's role? Or are they about equally homogeneous?

II. Exercises on random variables and probability distributions

(1) Let X follow the Bernoulli distribution with parameter π=0.56. Calculate E(X) and Var(X).

(2) Let S=the number of Obama supporters in a random sample of 11 voters, each of whom has a

probability of π=0.6 of voting for Obama. Provide the probability distribution of S. (Hint: Use

the table of “Individual Binomial Probabilities” in Wonnacott & Wonnacott.)

(3)For the random variable S in (2), calculate E(S) and Var(S).

(4)For the random sample of 11 voters in (2), what is the probability that a majority of them are

Obama supporters? What is the probability that a minority of them are Obama supporters?

1

## Document Summary

3 (due thursday, february 27: in 1984, a gallup survey asked a national sample of respondents: Recently there has been a lot of talk about women"s rights. Some people feel that women should have an equal role with men in running business, industry and government. Others feel that women should not generally have equal leadership roles and that even if they want to work they should still have primary responsibility for running the home and family. Responses to this question from men and women are summarized in the following frequency distributions: Exercises on random variables and probability distributions (1) let x follow the bernoulli distribution with parameter =0. 56. Calculate e(x) and var(x). (2) let s=the number of obama supporters in a random sample of 11 voters, each of whom has a probability of =0. 6 of voting for obama. Smalltown, u. s. a. , was known for its representativeness of the whole america in presidential vote.