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.
Left-tailed test, α = 0.09
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 7.1.24
Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
Ha: p = 0.25
H0: p ≠ 0.25
Verified step by step guidance1
Step 1: Understand the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, H0: p = 0.25 and Ha: p ≠ 0.25.
Step 2: Recall that the type of test (left-tailed, right-tailed, or two-tailed) is determined by the alternative hypothesis (Ha).
Step 3: Note that Ha: p ≠ 0.25 indicates that the test is looking for evidence that the population proportion (p) is not equal to 0.25. This means the test is concerned with deviations in both directions (greater than or less than 0.25).
Step 4: A hypothesis test that considers deviations in both directions is called a two-tailed test.
Step 5: Conclude that this is a two-tailed test because the alternative hypothesis uses the 'not equal to' (≠) symbol, which implies interest in both tails of the distribution.
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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 what we aim to support. The outcome of the test helps determine whether to reject the null hypothesis in favor of the alternative.
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06:21
Step 1: Write Hypotheses
Types of Hypothesis Tests
Hypothesis tests can be classified as left-tailed, right-tailed, or two-tailed based on the nature of the alternative hypothesis. A left-tailed test is used when Ha indicates that a parameter is less than a certain value, while a right-tailed test is used when Ha indicates that it is greater. A two-tailed test is employed when Ha suggests that the parameter is simply different from a specified value, allowing for deviations in both directions.
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06:21Step 1: Write Hypotheses
Understanding p-values
The p-value is a crucial component in hypothesis testing that helps determine the strength of the evidence against the null hypothesis. It represents the probability of observing the sample data, or something more extreme, assuming that the null hypothesis is true. A small p-value (typically less than 0.05) indicates strong evidence against H0, leading to its rejection in favor of Ha, while a larger p-value suggests insufficient evidence to reject H0.
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06:50Step 3: Get P-Value
Related Practice
Textbook Question
Finding a P-Value In Exercises 13–18, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance alpha.
Left-tailed test
z=-1.68
alpha=0.05
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
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.
Textbook Question
Explain how to test a population proportion p.
Textbook Question
In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.
Two-tailed test, α=0.05, n=27