Textbook Question
True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A large P-value in a test will favor rejection of the null hypothesis.
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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 7.1.13
Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.
σ ≠ 5
Verified step by step guidance1
Step 1: Understand the problem. The claim provided is σ ≠ 5, which is a statement about the population standard deviation (σ). In hypothesis testing, we need to define two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).
Step 2: Recall the definitions. The null hypothesis (H0) is typically a statement of no effect or no difference, and it often includes equality. The alternative hypothesis (Ha) is the complement of H0 and represents the claim being tested.
Step 3: Write the complement of the claim. The complement of σ ≠ 5 is σ = 5. This is because the null hypothesis must include equality, and the alternative hypothesis represents the inequality or difference.
Step 4: Assign the hypotheses. Based on the claim and its complement: H0: σ = 5 (null hypothesis) and Ha: σ ≠ 5 (alternative hypothesis).
Step 5: Verify the setup. Ensure that H0 and Ha are mutually exclusive and collectively exhaustive, meaning they cover all possible values of σ. This setup is correct for hypothesis testing.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject H0 in favor of Ha.
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06:21
Step 1: Write Hypotheses
Null and Alternative Hypotheses
The null hypothesis (H0) is a statement that indicates no significant difference or effect exists in the context of the study. In contrast, the alternative hypothesis (Ha) represents the claim that there is a significant difference or effect. For the statement σ ≠ 5, H0 would be σ = 5, while Ha would be σ ≠ 5, indicating that the population standard deviation is not equal to 5.
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06:21Step 1: Write Hypotheses
Complement of a Hypothesis
The complement of a hypothesis refers to the opposite scenario of the original claim. In hypothesis testing, if the null hypothesis states a specific condition (e.g., σ = 5), the complement would encompass all other possibilities (e.g., σ ≠ 5). Understanding the complement is crucial for correctly formulating both H0 and Ha, as it helps clarify the scope of the hypotheses being tested.
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4:23Complementary Events
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.
Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than \$320.
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Textbook Question
Hypothesis Testing Using Rejection Region(s) In Exercises 39–44, (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 z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
[APPLET] Gross Domestic Product A politician estimates that the mean gross domestic product (GDP) per country in a recent year is greater than \$400 billion. You want to test this estimate. To do so, you determine the GDPs of 42 randomly selected countries for that year. The results (in billions of dollars) are shown in the table at the left. Assume the population standard deviation is \$2099 billion. At alpha=0.06, can you support the politician’s estimate?
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Textbook Question
Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.
p < 0.45
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Textbook Question
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=81,α=0.10
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Textbook Question
In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.
Claim: μ≥8000; α=0.01. Sample statistics: x_bar=77,000, s=450, n=25
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