Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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2:16 minutes

Problem 6.4.6

Textbook Question

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.
c = 0.98, n = 26

Verified step by step guidance

Determine the degrees of freedom (df) for the chi-square distribution. The formula for degrees of freedom is df = n - 1, where n is the sample size. In this case, df = 26 - 1.

Identify the level of confidence (c) and calculate the corresponding significance level (α). The significance level is given by α = 1 - c. For c = 0.98, calculate α = 1 - 0.98.

Divide the significance level (α) into two tails for a two-tailed test. The left tail will have an area of α/2, and the right tail will also have an area of α/2.

Use a chi-square distribution table or statistical software to find the critical values. For the left critical value (χL²), find the chi-square value corresponding to an area of 1 - (α/2) to the left of the critical value. For the right critical value (χR²), find the chi-square value corresponding to an area of α/2 to the left of the critical value.

Write down the critical values χL² and χR² obtained from the table or software. These are the values that define the rejection region for the chi-square test at the given level of confidence.

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Key Concepts

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

Chi-Square Distribution

The Chi-Square distribution is a statistical distribution that is used primarily in hypothesis testing and in constructing confidence intervals for variance. It is defined by its degrees of freedom, which are determined by the sample size. In this context, the Chi-Square distribution helps in determining critical values that correspond to a specified level of confidence.

Critical Values

Critical values are the threshold points that define the boundaries of the acceptance region in hypothesis testing. They are determined based on the desired level of confidence and the distribution being used. For the Chi-Square distribution, critical values are used to assess whether the observed data falls within the expected range under the null hypothesis.

Level of Confidence

The level of confidence, denoted as 'c', represents the probability that the confidence interval will contain the true parameter value. A higher level of confidence indicates a wider interval, while a lower level results in a narrower interval. In this case, a confidence level of 0.98 means that we expect 98% of the intervals constructed from repeated samples to contain the true population parameter.

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Textbook Question

Does a population have to be normally distributed to use the chi-square distribution?

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Textbook Question

What happens to the shape of the chi-square distribution as the degrees of freedom increase?

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Textbook Question

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.99, n = 30

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Textbook Question

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Textbook Question

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Textbook Question

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Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.c = 0.98, n = 26

Key Concepts

Chi-Square Distribution

Critical Values

Level of Confidence

Watch next

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.
c = 0.98, n = 26