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