# You are conducting a multinomial hypothesis test (?? = 0.05) for the claim that all 5 categories...

## Question:

You are conducting a multinomial hypothesis test (?? = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Category Observed Frequency Expected Frequency A 6 B 16 C 15 D 13 E 20 Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations. What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.) ?2=?2= What are the degrees of freedom for this test? d.f.= What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) ?? greater than ?? This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. The sample data support the claim that all 5 categories are equally likely to be selected. There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected

## Chi-square test

The chi-square test is an important non-parametric test which determines the relationship between two or more variables. The chi-square test is also known as assumption-free test and the sample test statistics value is always expressed in a positive integer.

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Given information

• Level of significance: 0.05

The expected frequencies are calculated as:

{eq}\begin{align*} {\rm{Expected \ frequencies}}& =...

The Chi-Square Test

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Chapter 2 / Lesson 13
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What if you expect one thing, but get another? The chi-square test is a method of statistical analysis that can help us identify if the results from a genetic cross are simply due to chance, or if something else is happening. Learn about the chi-square test in this lesson.