{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch16 - Chapter 16 Chi Squared Tests 16.1 Introduction Two...

This preview shows pages 1–9. Sign up to view the full content.

Chi Squared Tests Chapter 16

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
16.1 Introduction Two statistical techniques are presented, to analyze nominal data. A goodness-of-fit test for the multinomial experiment. A contingency table test of independence. Both tests use the χ 2 as the sampling distribution of the test statistic.
The hypothesis tested involves the probabilities p 1 , p 2 , …, p k. of a multinomial distribution. The multinomial experiment is an extension of the binomial experiment. There are n independent trials. The outcome of each trial can be classified into one of k categories, called cells. The probability p i that the outcome fall into cell i remains constant for each trial. Moreover, p 1 + p 2 + … +p k = 1. Trials of the experiment are independent 16.2 Chi-Squared Goodness-of- Fit Test

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
16.2 Chi-squared Goodness-of- Fit Test We test whether there is sufficient evidence to reject a pre-specified set of values for p i. The hypothesis: i i k k a p one least At H a p a p a p H = = = : ,..., , : 1 2 2 1 1 0 The test builds on comparing actual frequency and the expected frequency of occurrences in all the cells.
Example 16.1 Two competing companies A and B have enjoy dominant position in the market. The companies conducted aggressive advertising campaigns. Market shares before the campaigns were: Company A = 45% Company B = 40% Other competitors = 15%. The multinomial goodness of fit test - Example

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 16.1 continued To study the effect of the campaign on the market shares, a survey was conducted. The multinomial goodness of fit test - Example 200 customers were asked to indicate their preference regarding the product advertised. Survey results: 102 customers preferred the company A’s product, 82 customers preferred the company B’s product,
The multinomial goodness of fit test - Example Example 16.1 continued Can we conclude at 5% significance level that the market shares were affected by the advertising campaigns?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Solution The population investigated is the brand preferences. The data are nominal (A, B, or other) This is a multinomial experiment (three categories).
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}