# Eleisha's Segment 32: Contingency Tables: A First Look

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To Calculate

1. 20 our of 100 U.S. Senators are women, yet when the Senate formed an intramural baseball team of 9 people only 1 woman was chosen for the team. What is the probability of this occurring by chance? What is the p-value with which the null hypothesis "there is no discrimination against women Senators" can be rejected?

2. A large jelly bean jar has 20% red jelly beans, 30% blue, and 50% yellow. If 6 jelly beans are chosen at random, what is the chance of getting exactly 2 of each color? What is the name of this distribution?

This is a multinomial distribution.

$\displaystyle N = 6, p_r = 0.2, p_b = 0.3, \text{and } p_y = 0.5$

Want to calculate, P, where P:

$\displaystyle P = \text{Prob}(\text{2 red, 2 blue, 2 yellow}| N, p_r, p_b, p_y) = \frac{6!}{2!2!2!}(0.2)^2(0.3)^2(0.5)^2 = 0.081$

3. A small jelly bean jar has 2 red jelly beans, 3 blue, and 5 yellow. If 6 jelly beans are chosen at random, what is the chance of getting exactly 2 of each color? What is the name of this distribution?

This is a Hypergeometrical Disbtribution Want to calculate:

$\displaystyle \text{Prob(2 red, 2 blue, 2 yellow} )$

To Think About

1. Suppose that, in the population, 82% of people are right-handed, 18% left handed; 49% are male, 51% female; and that handedness and sex are independent. Repeatedly draw samples of N=15 individuals, form the contingency table, and apply the chi-square test for significance to get a p-value, exactly as described in the lecture segment. How often is your p-value less than 0.05? If you get an answer that is different from 0.05, why? Try larger values of N until the answer converges to 0.05. (How are you handling zero draws when they occur?)

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