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Chapter 11: The Chi-Square Distribution

Introduction to Chapter 11: The Chi-Square Distribution

This is a photo of a pile of grocery store receipts. The items and prices are blurred.
Figure 11.1. The chi-square distribution can be used to find relationships between two things, like grocery prices at different stores. (credit: Pete/flickr)

Have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer these questions by conducting a hypothesis test.

You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.

In this chapter, you will learn the three major applications of the chi-square distribution:

  1. the goodness-of-fit test, which determines if data fit a particular distribution, such as in the lottery example
  2. the test of independence, which determines if events are independent, such as in the movie example
  3. the test of a single variance, which tests variability, such as in the coffee example

Note

Though the chi-square distribution depends on calculators or computers for most of the calculations, there is a table available. TI-83+ and TI-84 calculator instructions are included in the text.

To do the homework problems for this chapter, use the following solution sheet.

The Chi-Square Distribution Worksheet

  1. [latex]H_0: \underline{\hspace{2cm}}[/latex]
  2. [latex]H_a: \underline{\hspace{2cm}}[/latex]
  3. What are the degrees of freedom?
  4. State the distribution to use for the test.
  5. What is the test statistic?
  6. What is the p-value? In one to two complete sentences, explain what the p-value means for this problem.
  7. Use the previous information to sketch a picture of this situation. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p-value.
    This is a right-skewed frequency curve with blank horizontal and vertical axes.
  8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences.
    1. Alpha: [latex]\underline{\hspace{2cm}}[/latex]
    2. Decision: [latex]\underline{\hspace{2cm}}[/latex]
    3. Reason for decision: [latex]\underline{\hspace{2cm}}[/latex]
    4. Conclusion: [latex]\underline{\hspace{2cm}}[/latex]

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