Chapter 11: Additional Topics Using Inferences

11.1 – Chi-Square: Tests of Independence11.2 – Chi-Square: Goodness of Fit11.3 – Testing a Single Variance or Standard Deviation11.4 – Inferences for Correlation and Regression

Focus Problem

“Stone Age Tools and Archaeology”

• Read page 469 in text book

– Yes, it may be used in a HW problem!

11.1 – Chi-Square: Tests of Independence

Chi-Square: X2 – Not a bell-shaped curve, – The mode (high point) of the distribution with n

degrees of freedom occurs over (n-2)– We use this test to test the independence of 2

factors!!

Chi-Square Distribution

Ho : _______ and _______ are independent

H1 : _______ and _______ are NOT independent

Contingency Table

Expected Frequency

• Formula for expected frequency E

E =

Guided Exercise #1

• As whole group, turn to page 473– Look-over answers

– Whole group clarification

GE #1

Computing the Sample Test Statistic X2

Sample Statistic

Guided Exercise #2

• As whole group, turn to page 475– Look-over answers

– Whole group clarification

Degrees of Freedom

d.f. = (R – 1)(C – 1)

• R = number of cell rows• C = number of cell columns

Guided Exercise #3

• As whole group, turn to page 476– Look-over answers

– Whole group clarification

Finding the P-Value for Tests of Independence

Always Right TailedTable in back

How to Test for Independence of Two Statistical Variables

Same as before…1. Null Hypothesis, alternative hypothesis, level

of significance2. X2

3. P-value 4. Reject or not reject null hypothesis5. Conclude using context.

Guided Exercise #4

• As whole group, turn to page 478-479– Look-over answers

– Whole group clarification

Show on Calculator

Checkpoint

Prescott will lose!

Homework

• Read Pages 468-479– Take notes on what we have not covered

• Do Problems – Page 480-483 (1-10) ODD• Check odds in back of book

• Read and preload 11.2 information– Notes/vocab