View source for Segment 32. Contingency Tables: A First Look

====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.)

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

Links to the slides: [http://wpressutexas.net/coursefiles/32.ContingencyTablesFirstLook.pdf PDF file] or [http://wpressutexas.net/coursefiles/32.ContingencyTablesFirstLook.ppt 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 [[Media:Quiz20140409.pdf|here]].

We will analyze 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?

{|
! align="left"| 
! Vanilla
! Strawberry
! Chocolate
|-
!Texas Tech
|1
|1
|13
|-
!A&M
|16
|4
|15
|-
!UT
|45
|32
|80
|}

{|
! align="left"| Grades
!    A
!    B
!    C
!    D
|-
!A&M
|5
|24
|32
|1
|-
!UT
|17
|80
|50
|18
|}