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

Larson 8th Edition

Ch. 7 - Hypothesis Testing with One Sample

Problema 7.1.5

Capitolo 7, Problema 7.1.5

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.

In a hypothesis test, you assume the alternative hypothesis is true.

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Understand the key terms: In hypothesis testing, there are two hypotheses - the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis represents the default assumption or status quo, while the alternative hypothesis represents the claim or effect being tested.

Recall the assumption in hypothesis testing: In hypothesis testing, we always assume the null hypothesis (H₀) is true at the start of the test. This assumption allows us to calculate probabilities and test the evidence against H₀.

Evaluate the statement: The statement claims that in a hypothesis test, you assume the alternative hypothesis (H₁) is true. This is incorrect because the assumption is always based on the null hypothesis (H₀), not the alternative hypothesis.

Rewrite the statement as true: A correct version of the statement would be: 'In a hypothesis test, you assume the null hypothesis is true.'

Conclude: The original statement is false, and the corrected version clarifies the proper assumption in hypothesis testing.

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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), which represents a default position, and the alternative hypothesis (H1), which represents a new claim. The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.

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Percorso guidato

06:21

Step 1: Write Hypotheses

Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the starting point for the test. The alternative hypothesis (H1) is what the researcher aims to support, suggesting that there is an effect or a difference. It is crucial to understand that during the testing process, we assume the null hypothesis is true until evidence suggests otherwise.

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Percorso guidato

06:21

Step 1: Write Hypotheses

Assumption in Hypothesis Testing

In hypothesis testing, the assumption is that the null hypothesis is true at the beginning of the test. This means that the evidence collected from the sample data is used to evaluate whether there is sufficient support to reject the null hypothesis. The statement in the question is false because we do not assume the alternative hypothesis is true; rather, we start with the null hypothesis.

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Percorso guidato

06:21

Step 1: Write Hypotheses

Pratica correlata

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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.

Right-tailed test, α = 0.08

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Left-tailed test, α = 0.09

115

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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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Explain how to test a population proportion p.