# Chi-Square Distribution

1. When and how do you use a chi-square distribution to test if two variables are independent? Also, provide an example from your filed showing how you might use a contingency table for expected frequencies in your work.

2. How do you use the chi-square distribution to test if a frequency distribution fits a claimed distribution? Provide an example from your work showing the steps of the chi-square Goodness-of-Fit Test.

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#### Solution Preview

Hello Dear Student,

1. The Chi-square test is used when the dependent variable is a categorical variable or a nominal scale meaning that variables are in mutually exclusive classes or that the variables are only found within one category.

*For example, if I were to take a random sample of people what their major was they would respond by saying, either Psychology, Economics, Education etc. The majors are not overlapping in any way. So if you are going to use the chi-square test you are only working with independent variables. After you collected your data on the students' major (our hypothetical example continued), you would then use chi-square to determine if the numbers received are "high", "low" or "normal".

In general, the chi-square test is used to test whether the number of observations within categorical variables differs significantly from hypothetical conditions. The chi-square test utilizes Oi to indicate the observed frequencies within each class. T is also used within this test to ...

#### Solution Summary

The solution determines when and how to use a chi-square distribution to test if two variables are independent. Frequency distribution fits of a claim distribution is determined.

Chi Square Distribution with Degrees of Freedom

Chi-square distribution

Use the calculator provided to solve the following problems.

?Suppose that X2 follows a chi-square distribution with 7 degrees of freedom. Compute P (X2 <=5). Round your answer to at least three decimal places.

?Suppose again that X2 follows a chi-square distribution with 7 degrees of freedom. Find k such that P (X2 > k) = 0.1. Round your answer to at least two decimal places.

?Find the median of the chi-square distribution with 7 degrees of freedom. Round your answer to at least two decimal places.

See attached file.

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