Ch. 7 - Hypothesis Testing with One Sample

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 7 - Hypothesis Testing with One Sample

Problem 7.1.25

Chapter 7, Problem 7.1.25

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.

Tablets A tablet manufacturer claims that the mean life of the battery for a certain model of tablet is more than 8 hours.

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Identify the claim: The manufacturer claims that the mean life of the battery for the tablet is more than 8 hours. This is a statement about the population mean (μ).

Express the claim mathematically: The claim can be written as μ > 8, where μ represents the mean battery life in hours.

Define the null hypothesis (H₀): The null hypothesis is the statement that there is no effect or no difference. It is the complement of the claim and includes equality. Thus, H₀: μ ≤ 8.

Define the alternative hypothesis (H₁): The alternative hypothesis is the statement that supports the claim. Since the claim is that the mean battery life is more than 8 hours, H₁: μ > 8.

Identify which hypothesis represents the claim: The claim is represented by the alternative hypothesis (H₁: μ > 8). The null hypothesis (H₀: μ ≤ 8) is tested against this claim.

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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 there is no relationship between two measured phenomena. In this context, it would assert that the mean battery life of the tablet is 8 hours or less, providing a baseline for statistical testing.

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, it would claim that the mean battery life of the tablet is greater than 8 hours, representing the manufacturer's assertion and the focus of the statistical test.

Claim

A claim in hypothesis testing refers to the assertion made by the manufacturer that can be tested statistically. In this case, the claim is that the mean battery life exceeds 8 hours, which is represented by the alternative hypothesis, indicating the direction of the test and the expected outcome.

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Guided course

01:35

Step 1: Write Hypotheses Example 1

Related Practice

Textbook Question

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

Ha: μ ≥ 5.2

H0: μ < 5.2

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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

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Textbook Question

In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

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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=0.01, n=35

137

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Textbook Question

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Repeat Customers A used textbook selling website claims that at least 60% of its new customers will return to buy their next textbook.

101

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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.

Survey A polling organization reports that the number of responses to a survey mailed to 100,000 U.S. residents is not 100,000.

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