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
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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 7.2.8
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
Verified step by step guidance1
Step 1: Understand the problem. The P-value is a measure of the strength of evidence against the null hypothesis (H0). A smaller P-value indicates stronger evidence to reject H0. The decision to reject H0 depends on comparing the P-value to the significance level (α).
Step 2: Recall the decision rule. If the P-value is less than the significance level (α), reject the null hypothesis (H0). Otherwise, fail to reject H0.
Step 3: Compare the P-value (P = 0.0062) to the significance level α = 0.01. If P < α, reject H0; otherwise, fail to reject H0.
Step 4: Compare the P-value (P = 0.0062) to the significance level α = 0.05. If P < α, reject H0; otherwise, fail to reject H0.
Step 5: Compare the P-value (P = 0.0062) to the significance level α = 0.10. If P < α, reject H0; otherwise, fail to reject H0.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
P-Value
The P-value is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis (H0) is true. A smaller P-value indicates stronger evidence against H0, suggesting that the null hypothesis may be rejected.
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06:50
Step 3: Get P-Value
Null Hypothesis (H0)
The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. Researchers aim to gather evidence to either reject or fail to reject H0 based on the data collected. Understanding H0 is crucial for interpreting the results of a hypothesis test and the associated P-value.
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06:21Step 1: Write Hypotheses
Level of Significance (α)
The level of significance (α) is a threshold set by the researcher before conducting a hypothesis test, which determines the criteria for rejecting the null hypothesis. Common values for α are 0.01, 0.05, and 0.10. If the P-value is less than or equal to α, the null hypothesis is rejected, indicating that the results are statistically significant.
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Related Practice
Textbook Question
Explain how to test a population variance or a population standard deviation.
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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.
Left-tailed test, n=24,α=0.05
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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.
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Textbook Question
Hypothesis Testing Using Rejection Regions In Exercises 7–12, (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.
Nursing A patient care manager claims that more than half of all nurses feel they became better professionals during the coronavirus pandemic. In a random sample of 300 nurses, 174 say they became better professionals during the pandemic. At α=0.01, is there enough evidence to support the manager’s claim?
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Textbook Question
Hypothesis Testing Using a P-Value In Exercises 13–16, (a) identify the claim and state H0 and Ha, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim.
Stray Cats An animal advocate claims that 25% of U.S. households have taken in a stray cat. In a random sample of 500 U.S. households, 105 say they have taken in a stray cat. At α=0.05, is there enough evidence to reject the advocate’s claim?
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