Statistics - Chi-Square Testing
12/21/2013
VIETNAM NATIONAL UNIVERSITY – HOCHIMINH CITY INTERNATIONAL UNIVERSITY SCHOOL OF BUSINESS ADMINISTRATION ------o0o------
CHAPTER 14: CHI-SQUARE TESTING
STATISTICS FOR BUSINESS TAs: Vo Vuong Van Anh, Le Phuoc Thien Thanh, and Le Nhat Ho December 21, 2013
TABLE OF CONTENTS
• PART I: CHI-SQUARE TESTING FOR GOODNESS-OF-FIT. • PART II: CHI-SQUARE TESTING FOR NORMAL DISTRIBUTION. • PART III: CHI-SQUARE TESTING FOR INDEPENDENCE.
December 2013
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12/21/2013
Hypothesis Testing Procedure for Chi-Square Testing
5 Steps to Perform an Chi-Square Testing STEP 01 State the null and alternative hypotheses ( STEP 02 ) Determine the expected counts (frequencies of occurrence of certain events expected under the null hypothesis) and observed counts of data points falling in the different cells. Compute the test statistic value (based on the difference between the observed and the expected; Hint: Establishing a table) Find the critical value at the predetermined significance level. Draw conclusion by comparing the test statistic value and the critical value.
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STEP 03 STEP 04 STEP 05
December 2013
PART I: CHI-SQUARE TESTING FOR GOOODNESS-OF-FIT
• A goodness-of-fit chi-square test is a statistical test of how well our data support an assumption about the distribution of a population or random variable of interest. The test determines how well an assumed distribution fits the data.
December 2013
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12/21/2013
PART I: CHI-SQUARE TESTING FOR GOOODNESS-OF-FIT
PROBLEM:
A study reports an analysis of 35 key product categories. At the time of the study, 72.9% of the products sold were of a national brand, 23% were private label, and 4.1% were generic. Suppose that you want to test whether these percentages are still valid for the market today. You collect a random sample of 1,000 products in the 35 product categories studied, and you find the following: 610 products are of a
VIETNAM NATIONAL UNIVERSITY – HOCHIMINH CITY INTERNATIONAL UNIVERSITY SCHOOL OF BUSINESS ADMINISTRATION ------o0o------
CHAPTER 14: CHI-SQUARE TESTING
STATISTICS FOR BUSINESS TAs: Vo Vuong Van Anh, Le Phuoc Thien Thanh, and Le Nhat Ho December 21, 2013
TABLE OF CONTENTS
• PART I: CHI-SQUARE TESTING FOR GOODNESS-OF-FIT. • PART II: CHI-SQUARE TESTING FOR NORMAL DISTRIBUTION. • PART III: CHI-SQUARE TESTING FOR INDEPENDENCE.
December 2013
Powered by Vo Vuong Van Anh
2
1
12/21/2013
Hypothesis Testing Procedure for Chi-Square Testing
5 Steps to Perform an Chi-Square Testing STEP 01 State the null and alternative hypotheses ( STEP 02 ) Determine the expected counts (frequencies of occurrence of certain events expected under the null hypothesis) and observed counts of data points falling in the different cells. Compute the test statistic value (based on the difference between the observed and the expected; Hint: Establishing a table) Find the critical value at the predetermined significance level. Draw conclusion by comparing the test statistic value and the critical value.
Powered by Vo Vuong Van Anh 3
STEP 03 STEP 04 STEP 05
December 2013
PART I: CHI-SQUARE TESTING FOR GOOODNESS-OF-FIT
• A goodness-of-fit chi-square test is a statistical test of how well our data support an assumption about the distribution of a population or random variable of interest. The test determines how well an assumed distribution fits the data.
December 2013
Powered by Vo Vuong Van Anh
4
2
12/21/2013
PART I: CHI-SQUARE TESTING FOR GOOODNESS-OF-FIT
PROBLEM:
A study reports an analysis of 35 key product categories. At the time of the study, 72.9% of the products sold were of a national brand, 23% were private label, and 4.1% were generic. Suppose that you want to test whether these percentages are still valid for the market today. You collect a random sample of 1,000 products in the 35 product categories studied, and you find the following: 610 products are of a