Textbook Question
In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.
Two-tailed test, α=0.02, n=12
11
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
2:05 minutesProblem 7.RE.3
Textbook Question
n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.
p < 0.205
Verified step by step guidance1
Identify the claim in the problem. The claim is 'p < 0.205', which is a statement about the population proportion (p).
Understand that the complement of the claim is the opposite of the inequality. The complement of 'p < 0.205' is 'p ≥ 0.205'.
Determine which statement represents the null hypothesis (H0) and which represents the alternative hypothesis (Ha). The null hypothesis (H0) always includes equality or '≥', while the alternative hypothesis (Ha) represents the claim or the inequality 'p < 0.205'.
Assign the hypotheses: H0: p ≥ 0.205 (the complement) and Ha: p < 0.205 (the claim).
Conclude that the null hypothesis (H0) is the statement to be tested, while the alternative hypothesis (Ha) is what we aim to support if the evidence is sufficient.
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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 represents the claim that the population proportion is greater than or equal to 0.205, which is the opposite of the alternative hypothesis.
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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. For the given claim 'p < 0.205', the alternative hypothesis would be that the population proportion is indeed less than 0.205, indicating a specific direction of interest.
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06:21Step 1: Write Hypotheses
Complement of a Statement
The complement of a statement refers to the opposite scenario of the original claim. In this case, the complement of 'p < 0.205' is 'p ≥ 0.205', which encompasses all values that are not less than 0.205, thus providing a complete view of the possible outcomes in hypothesis testing.
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