Segment 32. Contingency Tables: A First Look

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Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

The direct YouTube link is http://youtu.be/NvCdN2RFufY

Links to the slides: PDF file or PowerPoint file

Problems

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?

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?

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?)

Class Activity

There was a surprise quiz. Bill's solutions are here.

We will analyze these contingency tables, asking (i) What is Failed to parse (unknown error): \chi^2 ? (ii) What is the p-value? (iii) Is there a significant association? (iv) If so, can you describe the main effect(s) seen?

Vanilla Strawberry Chocolate
Texas Tech 1 1 13
A&M 16 4 15
UT 45 32 80
Grades A B C D
A&M 5 24 32 1
UT 17 80 50 18