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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2:37 minutes

Problem 7.R.4

Textbook Question

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

μ ≠ 150,020

Verified step by step guidance

Step 1: Understand the problem. The given claim is μ ≠ 150,020, which is a statement about the population mean (μ). This is a two-tailed claim because it states that μ is not equal to a specific value.

Step 2: Recall the definitions of null hypothesis (H0) and alternative hypothesis (Ha). The null hypothesis (H0) is a statement of no effect or no difference, and it typically includes equality (e.g., =, ≤, or ≥). The alternative hypothesis (Ha) is the claim being tested and represents a statement of inequality (e.g., ≠, <, or >).

Step 3: Write the complement of the claim. The complement of μ ≠ 150,020 is μ = 150,020. This is because the complement of 'not equal to' is 'equal to.'

Step 4: Assign H0 and Ha. The null hypothesis (H0) will be the complement of the claim, so H0: μ = 150,020. The alternative hypothesis (Ha) will be the original claim, so Ha: μ ≠ 150,020.

Step 5: Summarize the hypotheses. The null hypothesis (H0) is μ = 150,020, and the alternative hypothesis (Ha) is μ ≠ 150,020. These hypotheses will be used in hypothesis testing to determine whether there is enough evidence to reject H0 in favor of Ha.

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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 asserts that the population mean (μ) is equal to a specific value, which is 150,020. Researchers aim to gather evidence against H0 to support an alternative hypothesis.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) represents a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this case, Ha is that the population mean (μ) is not equal to 150,020, indicating a significant deviation from this value. It is what researchers hope to support through their data analysis.

Complement of a Statement

The complement of a statement refers to the opposite of that statement. For the claim μ ≠ 150,020, the complement would be μ = 150,020. Understanding complements is crucial in hypothesis testing, as it helps clarify the relationship between the null and alternative hypotheses, ensuring a comprehensive approach to statistical analysis.

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Textbook Question

Getting at the Concept Explain why a level of significance of α=0 is not used.

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Textbook Question

Writing A null hypothesis is rejected with a level of significance of 0.10. Is it also rejected at a level of significance of 0.05? Explain.

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Textbook Question

Hypothesis Testing Using Rejection Regions In Exercises 23–30, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic X^2, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.

Salaries The annual salaries (in dollars) of 12 randomly chosen nursing supervisors are shown in the table at the left. At α=0.10, is there enough evidence to reject the claim that the standard deviation of the annual salaries is $18,630?

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Textbook Question

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

μ = 82

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Textbook Question

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

p ≥ 0.64

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Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Left-tailed test, α=0.05, n=48

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Textbook Question

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.

Left-tailed test, α=0.05, n=15

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Textbook Question

In Exercises 45–48, determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.

Claim: p≥0.04; α=0.10

Sample statistics: p_hat = 0.03, n=30

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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 ≠ 150,020

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 ≠ 150,020