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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2:07 minutes

Problem 7.RE.1

Textbook Question

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

μ ≤ 375

Verified step by step guidance

Understand the claim: The claim is that the population mean (μ) is less than or equal to 375. This will help us determine the null hypothesis (H0) and the alternative hypothesis (Ha).

Write the complement of the claim: The complement of 'μ ≤ 375' is 'μ > 375'. This is because the complement of 'less than or equal to' is 'greater than'.

Identify the null hypothesis (H0): The null hypothesis always includes the equality part of the claim. Therefore, H0: μ ≤ 375.

Identify the alternative hypothesis (Ha): The alternative hypothesis is the complement of the null hypothesis. Therefore, Ha: μ > 375.

Summarize the hypotheses: H0: μ ≤ 375 (the claim), and Ha: μ > 375 (the complement). These hypotheses will be used for statistical testing.

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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 case, H0 states that the population mean (μ) is less than or equal to 375, suggesting that any observed effect is due to sampling variability rather than a true effect.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) represents the claim that contradicts the null hypothesis, indicating the presence of an effect or difference. For the given statement, Ha would be μ > 375, suggesting that the population mean is greater than 375, which is what the researcher aims to provide evidence for.

Complement of a Statement

The complement of a statement refers to the opposite of that statement. In hypothesis testing, if the null hypothesis is μ ≤ 375, its complement would be μ > 375. Understanding the complement is crucial for formulating the alternative hypothesis and interpreting the results of statistical tests.

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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.μ ≤ 375

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.

μ ≤ 375