Skip to main content
Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.RE.1
Chapter 7, Problem 7.RE.1

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
1
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

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.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

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.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

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.
Recommended video:
4:23
Complementary Events
Related Practice
Textbook Question

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.


Two-tailed test, z = 2.57, α = 0.10

98
views
Textbook Question

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


p < 0.205

30
views
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

77
views
Textbook Question

In Exercises 55–58, test the claim about the population variance or standard deviation at the level of significance . Assume the population is normally distributed.


Claim: σ^2 > 2; α=0.10. Sample statistics: s^2 = 2.95, n=18

72
views
Textbook Question

In Exercises 51–54, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance.


Left-tailed test, n=6, α=0.05

103
views
Textbook Question

In Exercises 7–10, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.


An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

70
views