Textbook Question
Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.
Two-tailed test, α = 0.12
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 7.1.17
Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.
Ha: μ > 3
Verified step by step guidance1
Step 1: Understand the alternative hypothesis (Ha: μ > 3). This indicates that the mean μ is greater than 3, so the graph should represent values of μ greater than 3 with shading or emphasis to the right of 3.
Step 2: Analyze the provided graphs. Look for the graph where the shading or emphasis starts at 3 and extends to the right, representing μ > 3. In this case, the correct graph is option 'a'.
Step 3: State the null hypothesis (H0). The null hypothesis is the opposite of the alternative hypothesis, so H0: μ ≤ 3. This means the mean μ is less than or equal to 3.
Step 4: Sketch the graph for the null hypothesis. The graph should represent values of μ less than or equal to 3, with shading or emphasis to the left of 3.
Step 5: Verify the match between the alternative hypothesis and its graph, and ensure the null hypothesis graph is correctly sketched to represent the opposite scenario.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis (H0)
The null hypothesis is a statement that there is no effect or no difference, serving as a default position that indicates no change from a known value. In this case, it would state that the population mean (μ) is less than or equal to 3 (H0: μ ≤ 3). This hypothesis is tested against the alternative hypothesis to determine if there is enough evidence to reject it.
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Step 1: Write Hypotheses
Alternative Hypothesis (Ha)
The alternative hypothesis represents a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. Here, Ha: μ > 3 indicates that the population mean is greater than 3. This hypothesis is what researchers aim to support through statistical testing, often leading to a one-tailed test in this context.
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06:21Step 1: Write Hypotheses
Graphical Representation of Hypotheses
Graphical representations of hypotheses help visualize the relationship between the null and alternative hypotheses. In this case, the graph would illustrate the critical region for the alternative hypothesis (Ha: μ > 3) on the right side of the number line, indicating where we would reject the null hypothesis. Understanding how to sketch these graphs is crucial for interpreting statistical results.
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Related Practice
Textbook Question
Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
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Textbook Question
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Textbook Question
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Textbook Question
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Textbook Question
Hypothesis Testing Using Rejection Regions In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.
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