Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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2:31 minutes

Problem 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 guidance

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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Key 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.

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.

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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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.

Key Concepts

Null Hypothesis

Alternative Hypothesis

Mathematical Representation of Hypotheses

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