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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 7.1.27
Chapter 7, Problem 7.1.27

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.


Base Price of an ATV The standard deviation of the base price of an all-terrain vehicle is no more than \$320.

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Understand the problem: The claim is that the standard deviation of the base price of an all-terrain vehicle (ATV) is no more than \$320. This means the claim is about the population standard deviation (σ).
Express the claim mathematically: The claim can be written as σ ≤ 320, where σ represents the population standard deviation.
Define the null hypothesis (H₀): The null hypothesis is typically the statement of equality or the status quo. In this case, H₀: σ ≤ 320.
Define the alternative hypothesis (H₁): The alternative hypothesis is the complement of the null hypothesis and represents the statement being tested. Here, H₁: σ > 320.
Identify the claim: Since the claim is that the standard deviation is no more than \$320, it corresponds to the null hypothesis (H₀).

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Key Concepts

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

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that assumes any observed variation is due to chance. In this context, it asserts that the standard deviation of the base price of an ATV is less than or equal to $320, which is a claim that needs to be tested.
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Step 1: Write Hypotheses

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, the alternative hypothesis would state that the standard deviation of the base price of an ATV is greater than $320, indicating a significant deviation from the null hypothesis.
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Step 1: Write Hypotheses

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing a framework for making inferences about population parameters.
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Step 1: Write Hypotheses
Related Practice
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 ≤ 645

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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 large P-value in a test will favor rejection of the null hypothesis.

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Textbook Question

How do the critical values for a two-tailed test change as alpha decreases?

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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] Gross Domestic Product A politician estimates that the mean gross domestic product (GDP) per country in a recent year is greater than \$400 billion. You want to test this estimate. To do so, you determine the GDPs of 42 randomly selected countries for that year. The results (in billions of dollars) are shown in the table at the left. Assume the population standard deviation is \$2099 billion. At alpha=0.06, can you support the politician’s estimate?


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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 ≠ 5

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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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