Skip to main content
Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.1.16
Chapter 7, Problem 7.1.16

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

Verified step by step guidance
1
Identify the claim in the problem. The claim is that the population proportion is equal to 0.21, which can be written as p = 0.21.
Write the complement of the claim. The complement of 'p = 0.21' is 'p ≠ 0.21', as the complement represents all values not equal to 0.21.
Determine which statement is the null hypothesis (H₀). The null hypothesis always includes equality, so H₀: p = 0.21.
Determine which statement is the alternative hypothesis (Hₐ). The alternative hypothesis is the complement of the null hypothesis, so Hₐ: p ≠ 0.21.
Summarize the hypotheses: H₀: p = 0.21 (the claim) and Hₐ: p ≠ 0.21 (the complement).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

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.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

Null and Alternative Hypotheses

The null hypothesis (H0) is a statement that indicates no change or no effect, serving as a default position that there is no relationship between variables. The alternative hypothesis (Ha) is the statement that reflects the claim or effect that the researcher aims to support. In the context of the given question, H0 would state that the population proportion p is equal to 0.21, while Ha would state that p is not equal to 0.21.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite of the original statement. In hypothesis testing, if the null hypothesis states a specific value (e.g., p = 0.21), the complement would encompass all other possibilities (e.g., p ≠ 0.21). Understanding the complement is crucial for correctly formulating the alternative hypothesis and interpreting the results of the hypothesis test.
Recommended video:
4:23
Complementary Events
Related Practice
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=4915; α=0.01. Sample statistics: x_bar=5017, s=5613, n=51

111
views
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.


Changing Jobs A researcher claims that 40% of U.S. adults would consider changing jobs. In a random sample of 50 U.S. adults, 25 say they would consider changing jobs. At α=0.10, is there enough evidence to reject the researcher’s claim?

77
views
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.


μ < 128

47
views
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?

104
views
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.

72
views
Textbook Question

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

100
views