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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1:54 minutes

Problem 7.RE.5

Textbook Question

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

σ > 1.9

Verified step by step guidance

Understand the problem: The claim is about the population standard deviation (σ) being greater than 1.9. We need to write the complement of this claim and identify which hypothesis is the null hypothesis (H₀) and which is the alternative hypothesis (Hₐ).

Recall the definitions: The null hypothesis (H₀) is a statement of no effect or equality, and it is the hypothesis we assume to be true unless there is strong evidence against it. The alternative hypothesis (Hₐ) is the claim we are testing and is typically the statement of inequality or difference.

Write the complement of the claim: The complement of 'σ > 1.9' is 'σ ≤ 1.9'. This represents all values of the standard deviation that are less than or equal to 1.9.

Assign the hypotheses: The null hypothesis (H₀) is the complement of the claim, so H₀: σ ≤ 1.9. The alternative hypothesis (Hₐ) is the claim itself, so Hₐ: σ > 1.9.

Summarize the hypotheses: H₀: σ ≤ 1.9 (null hypothesis), Hₐ: σ > 1.9 (alternative hypothesis). These hypotheses will be used in hypothesis testing to determine whether there is sufficient evidence to support the claim.

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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 standard deviation (σ) is less than or equal to 1.9, suggesting that any observed effect is due to sampling variability rather than a true effect.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, indicating the presence of an effect or difference. For the given claim σ > 1.9, Ha asserts that the population standard deviation is greater than 1.9, suggesting a significant deviation from the null hypothesis that warrants further investigation.

Complement of a Statement

The complement of a statement refers to the opposite condition of that statement. In hypothesis testing, if the claim is σ > 1.9, the complement would be σ ≤ 1.9. Understanding complements is crucial for defining the null and alternative hypotheses, as they represent all possible outcomes in the context of the statistical test.

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n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.σ > 1.9

Key Concepts

Null Hypothesis (H0)

Alternative Hypothesis (Ha)

Complement of a Statement

Watch next

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

σ > 1.9