Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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1:24 minutes

Problem 7.1.9

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.

Verified step by step guidance

Understand the concept of a P-value: The P-value in hypothesis testing measures the probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true.

Recall the decision rule for hypothesis testing: A small P-value (typically less than the significance level, α, such as 0.05) provides evidence to reject the null hypothesis. Conversely, a large P-value suggests insufficient evidence to reject the null hypothesis.

Analyze the statement: The statement claims that a large P-value favors rejection of the null hypothesis. This contradicts the decision rule, as a large P-value indicates that the null hypothesis is likely true or that there is insufficient evidence to reject it.

Rewrite the statement as true: A correct version of the statement would be, 'A large P-value in a test suggests insufficient evidence to reject the null hypothesis.'

Conclude: The original statement is false, and the corrected version clarifies the relationship between P-values and hypothesis testing decisions.

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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 the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, while a larger P-value suggests weaker evidence.

Null Hypothesis

The null hypothesis is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. Researchers aim to test this hypothesis against an alternative hypothesis, which posits that there is an effect or a difference. The outcome of the test will either lead to the rejection or failure to reject the null hypothesis based on the evidence provided by the data.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves formulating a null hypothesis and an alternative hypothesis, calculating a test statistic, and determining the P-value to assess the strength of evidence against the null hypothesis. The decision to reject or not reject the null hypothesis is made based on the P-value in relation to a predetermined significance level.

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Related Practice

Textbook Question

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.

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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.

In a hypothesis test, you assume the alternative hypothesis is true.

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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 statistical hypothesis is a statement about a sample.

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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.

The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

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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.

To support a claim, state it so that it becomes the null hypothesis.

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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.

σ^2 ≥ 1.2

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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

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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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.

Key Concepts

P-value

Null Hypothesis

Hypothesis Testing

Watch next

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.