Ch 10 Chi-Square Distribution Hypothesis testing with tables. 2 way tables and 3 way tables.

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Presentation transcript:

Ch 10 Chi-Square Distribution Hypothesis testing with tables. 2 way tables and 3 way tables.

2 way table (2 variables) College Admission MaleFemale Admit3520 Deny4540

3 Way Tables (3 Variables) Math Program English Program MaleFemal e MaleFemal e Admit30105 Deny College Admission

X 2 Chi-Square Distribution 2 types Contingency tables Goodness-of-Fit test

Contingency Tables Testing the relation of the variable on a two way table.

IncreaseSameDecrease Course Book No prep SAT Scores compared to type of preparation H o There is no association with the method of SAT prep and the difference in test scores. H a There is an association with the method of SAT prep and the test score.

Critical Value Chi-Square Distribution Always right tail Degrees of Freedom = (r-1)(c-1) r is the number of rows c is the number of columns

IncreaseSameDecrease Course Book No prep Finding the expected values IncreaseSameDecrease Course Book No prep

Test Score IncreaseSameDecrease Course Book No prep

MaleFemale Pass Fail3429 Passing High School

Rule: Every expected value must be 5 or greater for the test to be valid.

Below is a table showing the letter grade a person received for a class and the number of days they were absent. Test at a 99% confidence level for association. <11 to 34 to 6>7 A B C D E Days absent from class. Letter grade H o There is no association between the number of days absent from class and your letter grade. H a There is an association between the number of days absent from class and your letter grade.

Goodness-of-Fit Test Test the claims that involves more than one proportion.

A roulette wheel has three different colors on it and each color has an equal chance of getting hit. Test the claim being 95% confident. Observed Red141 Black150 Green9 H o Red=Black=Green H a At least one is not equal to the rest. Test Score Degrees of freedom = n-1

Joe Bets thinks the closer a horse is when he starts a race the better chance he has of winning. Below he made a list of the chances the horses have of winning depending on where they start. Test Joe’s claim at 99% PositionChanceObserve d 130% %42 14%41 13%38 8%20 8%14 77%14 85%16 H o P1=30% P2=15% P3=14% P4=13% P5=8% P6=8% P7=7% P8=5% H a At least one is incorrect Degrees of Freedom = n-1