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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.5.12
Chapter 7, Problem 7.5.12

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.


Two-tailed test, n=61,α=0.01

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Determine the degrees of freedom (df) for the chi-square test. The formula for degrees of freedom is df = n - 1, where n is the sample size. In this case, df = 61 - 1.
Identify the level of significance (α) for the test. Here, α = 0.01, and since it is a two-tailed test, the significance level is split equally between the two tails (α/2 for each tail).
Use a chi-square distribution table or statistical software to find the critical values corresponding to the degrees of freedom (df = 60) and the significance levels (α/2 = 0.005 for each tail).
Define the rejection regions based on the critical values. For a two-tailed test, the rejection regions are: (1) the left tail, where the chi-square statistic is less than the lower critical value, and (2) the right tail, where the chi-square statistic is greater than the upper critical value.
Summarize the critical values and rejection regions. Clearly state the lower and upper critical values and describe the conditions under which the null hypothesis would be rejected.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Chi-Square Test

The chi-square test is a statistical method used to determine if there is a significant association between categorical variables. It compares the observed frequencies in each category to the frequencies expected under the null hypothesis. This test is commonly used in hypothesis testing to assess goodness-of-fit or independence.
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Critical Value

A critical value is a threshold that determines the boundary for rejecting the null hypothesis in hypothesis testing. It is derived from the chosen significance level (α) and the distribution of the test statistic. For a chi-square test, critical values can be found using chi-square distribution tables based on the degrees of freedom and the specified α level.
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Rejection Region

The rejection region is the range of values for the test statistic that leads to the rejection of the null hypothesis. In a two-tailed test, this region is split between both tails of the distribution. For a chi-square test with a significance level of α, the rejection regions are determined by the critical values, indicating where the test statistic must fall to reject the null hypothesis.
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Step 4: State Conclusion
Related Practice
Textbook Question

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