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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.R.6
Chapter 7, Problem 7.R.6

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


p ≥ 0.64

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Step 1: Understand the problem. The claim provided is 'p ≥ 0.64', where 'p' represents the population proportion. This is a hypothesis testing problem, and we need to identify the null hypothesis (H0) and the alternative hypothesis (Ha).
Step 2: Recall the definitions of H0 and Ha. The null hypothesis (H0) is a statement of no effect or no difference, and it always includes equality (e.g., '=', '≥', or '≤'). The alternative hypothesis (Ha) is the complement of H0 and represents what we are trying to find evidence for.
Step 3: Write the complement of the claim. The complement of 'p ≥ 0.64' is 'p < 0.64'. This is because the complement of 'greater than or equal to' is 'less than'.
Step 4: Assign H0 and Ha. Since the claim is 'p ≥ 0.64', this will be the null hypothesis (H0). The alternative hypothesis (Ha) will be the complement, which is 'p < 0.64'.
Step 5: Finalize the hypotheses. Write them as follows: H0: p ≥ 0.64 and Ha: p < 0.64. These hypotheses are now ready to be used in a hypothesis testing procedure.

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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 (H0) is a statement that indicates no effect or no difference, serving as a default position in statistical testing. In this context, it typically represents the status quo or a claim that a parameter, such as a population proportion, is equal to a specific value. For the given claim 'p ≥ 0.64', the null hypothesis would assert that 'p = 0.64'.
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Step 1: Write Hypotheses

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents the claim that researchers aim to support through statistical evidence. In this case, the alternative hypothesis would be 'p < 0.64', indicating that the population proportion is less than 0.64.
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Complement of a Statement

The complement of a statement refers to the opposite scenario of the original claim. In hypothesis testing, the complement helps to define the alternative hypothesis. For the claim 'p ≥ 0.64', the complement would be 'p < 0.64', which is essential for determining the alternative hypothesis in this statistical context.
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