# Segment 32. Contingency Tables: A First Look

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### 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

We analyzed these contingency tables, asking (i) What is <math>\chi^2</math>? (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 |