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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: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblema 7.1.8
Capitolo 7, Problema 7.1.8

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.


The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

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Understand the concept of the level of significance: The level of significance, denoted as \( \alpha \), is the threshold probability set by the researcher to determine whether to reject the null hypothesis. It represents the maximum probability of making a Type I error, which occurs when the null hypothesis is rejected even though it is true.
Analyze the given statement: The statement claims that the level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true. This aligns with the definition of \( \alpha \), as it is indeed the maximum probability of making a Type I error.
Determine if the statement is true or false: Based on the definition of the level of significance, the statement is true because it correctly describes \( \alpha \).
If the statement were false, rewrite it as a true statement: Since the statement is true, no rewriting is necessary. However, if it were false, you would need to clarify the definition of \( \alpha \) and its role in hypothesis testing.
Conclude the analysis: Confirm that the statement is true and explain why it aligns with the statistical concept of the level of significance.

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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 in a given situation. It serves as a baseline for statistical testing, where researchers aim to determine if there is enough evidence to reject this hypothesis in favor of an alternative hypothesis.
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Step 1: Write Hypotheses

Level of Significance

The level of significance, often denoted as alpha (α), is the threshold probability set by researchers to determine whether to reject the null hypothesis. It represents the maximum acceptable risk of making a Type I error, which occurs when the null hypothesis is incorrectly rejected when it is true. Common levels of significance are 0.05, 0.01, and 0.10.
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Step 4: State Conclusion Example 4

Type I Error

A Type I error occurs when a true null hypothesis is incorrectly rejected, leading to a false positive conclusion. This error is directly related to the level of significance; a lower alpha reduces the likelihood of a Type I error but may increase the risk of a Type II error, which is failing to reject a false null hypothesis.
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Types of Data
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Finding Critical Values and Rejection Regions In Exercises 23–28, find the critical value(s) and rejection region(s) for the type of z-test with level of significance α. Include a graph with your answer.


Two-tailed test, α = 0.12

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Getting at the Concept Explain why a level of significance of α=0 is not used.

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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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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.


High School Graduation Rate A high school claims that its mean graduation rate is more than 97%.

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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.


Credit Card Debt A credit reporting agency claims that the mean credit card debt in Colorado is greater than \$5540 per borrower. You want to test this claim. You find that a random sample of 30 borrowers has a mean credit card debt of \$5594 per person and a standard deviation of \$597 per person. At , can you support the claim α=0.05?

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Explain the difference between the z-test for μ using a P-value and the z-test for μ using rejection region(s).

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