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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 7.1.10
Chapter 7, Problem 7.1.10

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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1
Understand the null hypothesis (H₀): The null hypothesis is a statement of no effect, no difference, or the status quo. It is the hypothesis that researchers aim to test against the alternative hypothesis (H₁).
Recognize the purpose of the null hypothesis: The null hypothesis is typically formulated to be tested and potentially rejected in favor of the alternative hypothesis. It is the default assumption.
Evaluate the statement: The problem suggests that to support a claim, it should be stated as the null hypothesis. This is not always true. In many cases, the claim is stated as the alternative hypothesis (H₁), and the null hypothesis (H₀) represents the opposite of the claim.
Rewrite the statement if false: A more accurate statement would be, 'To support a claim, state it so that it becomes the alternative hypothesis, and the null hypothesis represents the opposite of the claim.'
Conclude: The original statement is false because claims are typically stated as the alternative hypothesis, not the null hypothesis. The null hypothesis is tested to determine whether there is enough evidence to support the alternative hypothesis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis

The null hypothesis is a fundamental concept in statistics that represents a default position or statement that there is no effect or no difference. It is typically denoted as H0 and serves as a starting point for statistical testing. Researchers aim to gather evidence to either reject or fail to reject the null hypothesis based on sample data.
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Step 1: Write Hypotheses

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) and the alternative hypothesis (H1). The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative, often using a significance level to guide the decision.
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Step 1: Write Hypotheses

Claim Support

Supporting a claim in statistics involves providing evidence that either supports or contradicts a hypothesis. When a claim is made, it is often framed in a way that can be tested statistically. If the claim is to be supported, it should be articulated as an alternative hypothesis, while the null hypothesis remains the statement of no effect or difference, which is tested against the evidence.
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Step 4: State Conclusion Example 4
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

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.

Textbook Question

Hypothesis Testing Using Rejection Region(s) In Exercises 39–44, (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.


[APPLET] Fluorescent Lamps A compact fluorescent lamp (CFL) bulb manufacturer guarantees that the mean life of a CFL bulb is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of 32 CFL bulbs. The results (in hours) are listed. Assume the population standard deviation is 1850 hours. At alpha=0.11, do you have enough evidence to reject the manufacturer’s claim?


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.


Left-tailed test, α=0.10, n=20

Textbook Question

Hypothesis Testing Using Rejection Regions In Exercises 19–26, (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 t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.


Lead Levels As part of your work for an environmental awareness group, you want to test a claim that the mean amount of lead in the air in U.S. cities is less than 0.032 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.021 microgram per cubic meter and the standard deviation is 0.034 microgram per cubic meter. At α=0.01, can you support the claim?

Textbook Question

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.


Ha: μ ≤ 8.0

H0: μ > 8.0