Textbook Question
In Exercises 7–10, (d) explain how you should interpret a decision that rejects the null hypothesis.
An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.
64
views
Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 7, Problem 7.RE.5
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 guidance1
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.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas 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 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.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses
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.
Recommended video:
Guided course
06:21Step 1: Write Hypotheses
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.
Recommended video:
4:23Complementary Events
Related Practice
Textbook Question
In Exercises 7–10, explain how you should interpret a decision that fails to reject the null hypothesis.
A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than \$2900.
37
views
Textbook Question
In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.
Left-tailed test, α=0.02
95
views
Textbook Question
[APPLET] A researcher claims that the mean age of the residents of a small town is more than 38 years. The ages (in years) of a random sample of 30 residents are listed below. At α=0.10, is there enough evidence to support the researcher’s claim? Assume the population standard deviation is 9 years.
370
views
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
You want your test to support a positive claim about your college, not just fail to reject one. Should you state your claim so that the null hypothesis contains the claim or the alternate hypothesis contains the claim? Explain.
77
views