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 = 0.21
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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 7.2.7
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 = 0.0838
Verified step by step guidance1
Step 1: Recall the decision rule for hypothesis testing. If the P-value is less than or equal to the level of significance (α), reject the null hypothesis (H₀). Otherwise, fail to reject H₀.
Step 2: Compare the given P-value (P = 0.0838) to the first level of significance, α = 0.01. Determine whether P ≤ α or P > α.
Step 3: Compare the given P-value (P = 0.0838) to the second level of significance, α = 0.05. Determine whether P ≤ α or P > α.
Step 4: Compare the given P-value (P = 0.0838) to the third level of significance, α = 0.10. Determine whether P ≤ α or P > α.
Step 5: Based on the comparisons in Steps 2, 3, and 4, state whether to reject or fail to reject H₀ for each level of significance (α = 0.01, 0.05, and 0.10).
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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 lower P-value indicates stronger evidence against H0, while a higher P-value suggests weaker evidence.
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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, H0 is rejected; if it is greater, H0 is not rejected. This concept is essential for making informed decisions based on statistical evidence.
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Related Practice
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.
Vaccinations In 2021, a reporter claims that at least 55% of U.S. adults feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. In a random sample of 200 U.S. adults, 56% feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. At α=0.10, is there enough evidence to reject the reporter’s claim?
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Textbook Question
Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.
Lung Cancer A report claims that lung cancer accounts for 25% of all cancer diagnoses.
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Textbook Question
Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.
Golf A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is less than 2.1 strokes.
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Textbook Question
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
a.
b.
c.
d.
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Textbook Question
In Exercise 1, you rejected the claim that p=0.53. But this claim was true. What type of error is this?
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