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 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
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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2:29 minutes

Problem 8.10

Textbook Question

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

μ≠2.28

Verified step by step guidance

Identify the claim in the problem. The claim is μ≠2.28, which is a statement about the population mean (μ). This indicates that the mean is not equal to 2.28.

Understand the complement of the claim. The complement of μ≠2.28 is μ=2.28, which states that the population mean is equal to 2.28.

Determine the null hypothesis (Ho). The null hypothesis always represents the statement of equality, so Ho: μ=2.28.

Determine the alternative hypothesis (Ha). The alternative hypothesis represents the claim being tested, so Ha: μ≠2.28.

Summarize the hypotheses: Ho: μ=2.28 (null hypothesis) and Ha: μ≠2.28 (alternative hypothesis). The alternative hypothesis is the claim, and the null hypothesis is its complement.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis (Ho)

The null hypothesis, denoted as Ho, is a statement that indicates no effect or no difference in a statistical test. It serves as the default assumption that any observed effect is due to sampling variability. In this case, the null hypothesis would be that the population mean μ equals 2.28.

Alternative Hypothesis (Ha)

The alternative hypothesis, represented as Ha, is a statement that contradicts the null hypothesis. It suggests that there is an effect or a difference. For the given claim μ≠2.28, the alternative hypothesis would be that the population mean μ is not equal to 2.28, indicating a significant deviation from this value.

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite scenario of the original claim. In hypothesis testing, if the null hypothesis states a specific value, the complement would encompass all other possibilities. For the claim μ≠2.28, the complement is μ=2.28, which is the condition under which the null hypothesis holds true.

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In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.μ≠2.28

Key Concepts

Null Hypothesis (Ho)

Alternative Hypothesis (Ha)

Complement of a Hypothesis

Watch next

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.

μ≠2.28