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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 7.1.30
Chapter 7, Problem 7.1.30

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.


College Debt According to a recent survey, 14% of adults currently carry student loan debt.

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Identify the parameter of interest: The problem is about the proportion of adults who currently carry student loan debt. Let the parameter be denoted as p, where p represents the true proportion of adults with student loan debt.
Translate the claim into a mathematical statement: The claim is that 14% of adults currently carry student loan debt. Mathematically, this is written as p = 0.14.
State the null hypothesis (H₀): The null hypothesis is a statement of no change or no effect. It is typically written as H₀: p = 0.14, which aligns with the claim in this case.
State the alternative hypothesis (H₁): The alternative hypothesis is the complement of the null hypothesis and depends on the context of the problem. If the problem does not specify a direction (greater than or less than), we use a two-tailed test. Thus, H₁: p ≠ 0.14.
Identify which hypothesis represents the claim: Since the claim is that 14% of adults carry student loan debt, and this matches the null hypothesis (H₀: p = 0.14), the null hypothesis represents the 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 assumes any observed effect is due to sampling variability. In this context, it would assert that the proportion of adults with student loan debt is equal to 14%, symbolically represented as H0: p = 0.14.
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06:21
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, it would claim that the proportion of adults with student loan debt is not equal to 14%, represented as H1: p ≠ 0.14, indicating a potential change in the debt situation.
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06:21
Step 1: Write Hypotheses

Claim

In hypothesis testing, the claim is the assertion that is being tested, often aligned with the alternative hypothesis. In this case, the claim is that the proportion of adults carrying student loan debt differs from 14%, which is encapsulated in the alternative hypothesis, H1.
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Step 1: Write Hypotheses Example 1
Related Practice
Textbook Question

Can a critical value for the chi-square test be negative? Explain.

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Textbook Question

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P= 0.2802


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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^2 ≥ 1.2

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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.


Two-tailed test, n=61,α=0.01

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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.


Security A campus security department publicizes that at most 25% of applicants become campus security officers.

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Textbook Question

The mean of a random sample of 18 test scores is x_bar. The standard deviation of the population of all test scores is sigma= 6. Under what condition can you use a z-test to decide whether to reject a claim that the population mean is mu=88?

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