Textbook Question
In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p <0.12, α=0.01. Sample statistics: p_hat = 0.10, n=40
Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 7, Problem 7.5.10
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.
Left-tailed test, n=24,α=0.05
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Identify 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 = 24 - 1 = 23.
Determine the type of test. Since this is a left-tailed test, the critical value will be located in the left tail of the chi-square distribution.
Use the chi-square distribution table or statistical software to find the critical value corresponding to df = 23 and α = 0.05. For a left-tailed test, the critical value is the chi-square value where the cumulative probability equals α.
Define the rejection region. For a left-tailed test, the rejection region consists of all chi-square values less than the critical value obtained in the previous step.
Summarize the results. State the critical value and the rejection region clearly, ensuring they align with the left-tailed test and the given level of significance.
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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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Intro to Least Squares Regression
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 left-tailed chi-square test, the critical value indicates the point below which the test statistic must fall to reject the null hypothesis.
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Rejection Region
The rejection region is the set of values for the test statistic that leads to the rejection of the null hypothesis. In a left-tailed test, this region is located to the left of the critical value on the chi-square distribution. If the calculated test statistic falls within this region, it suggests that the observed data is unlikely under the null hypothesis.
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09:56Step 4: State Conclusion
Related Practice
Textbook Question
In Exercises 29–32, test the claim about the population mean at the level of significance α. Assume the population is normally distributed.
Claim: ; μ ≠ 5880; α = 0.03; α = 413
Sample statistics: x_bar = 5771, n = 67
Textbook Question
In Exercises 15–22, test the claim about the population variance or standard deviation at the level of significance Assume the population is normally distributed.
Claim: σ<40, α=0.01 . Sample statistics: s=40.8, n=12
Textbook Question
Explain how to test a population variance or a population standard deviation.
Textbook Question
Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.
P = 0.0062
Textbook Question
Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.