Textbook Question
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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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
2:31 minutesProblem 7.1.28
Textbook Question
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.
Attendance An amusement park claims that the mean daily attendance at the park is at least 20,000 people.
Verified step by step guidance1
Understand the problem: The amusement park claims that the mean daily attendance is at least 20,000 people. This is the claim we need to translate into a mathematical statement and then formulate the null and alternative hypotheses.
Express the claim mathematically: The claim 'at least 20,000 people' means the mean daily attendance (denoted as μ) is greater than or equal to 20,000. Mathematically, this is written as μ ≥ 20,000.
Define the null hypothesis (H₀): The null hypothesis always includes equality. Since the claim involves 'at least,' the null hypothesis is H₀: μ ≥ 20,000.
Define the alternative hypothesis (H₁): The alternative hypothesis is the complement of the null hypothesis. Since the null states 'μ ≥ 20,000,' the alternative hypothesis is H₁: μ < 20,000.
Identify the claim: The claim is represented by the null hypothesis (H₀: μ ≥ 20,000) because it directly aligns with the amusement park's statement.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis
The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean daily attendance at the amusement park is 20,000 or more, which is the claim being tested.
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Step 1: Write Hypotheses
Alternative Hypothesis
The alternative hypothesis (H1) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, the alternative hypothesis would state that the mean daily attendance is less than 20,000, representing the possibility that the park's claim is not true.
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Mathematical Representation of Hypotheses
Mathematical representation of hypotheses involves formulating the null and alternative hypotheses in a precise manner using symbols. For this example, the null hypothesis can be expressed as H0: μ ≥ 20,000, while the alternative hypothesis can be expressed as H1: μ < 20,000, where μ represents the mean daily attendance.
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