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.
Two-tailed test, α=0.05, n=20
Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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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.10a
In Exercises 7–10, state the null and alternative hypotheses and identify which represents the claim,
An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.
Verified step by step guidance1
Identify the claim: The energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25. This is the basis for the alternative hypothesis.
Define the null hypothesis (H₀): The null hypothesis always represents the statement of no effect or no difference. In this case, it would state that the mean number of grams of carbohydrates in one bar is greater than or equal to 25. Mathematically, H₀: μ ≥ 25.
Define the alternative hypothesis (H₁): The alternative hypothesis represents the claim being tested. Here, it states that the mean number of grams of carbohydrates in one bar is less than 25. Mathematically, H₁: μ < 25.
Determine which hypothesis represents the claim: Since the claim is that the mean is less than 25, the alternative hypothesis (H₁) represents the claim.
Summarize the hypotheses: Null hypothesis (H₀): μ ≥ 25. Alternative hypothesis (H₁): μ < 25. The claim is represented by the alternative hypothesis.
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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 is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean number of grams of carbohydrates in an energy bar is equal to or greater than 25 grams.
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06:21
Step 1: Write Hypotheses
Alternative Hypothesis (H1)
The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this case, it posits that the mean number of grams of carbohydrates in an energy bar is less than 25 grams, which is the claim made by the energy bar maker.
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06:21Step 1: Write Hypotheses
Claim
A claim in hypothesis testing refers to a statement that is being tested for validity. In this scenario, the claim is that the mean carbohydrate content in the energy bars is less than 25 grams, which is represented by the alternative hypothesis, indicating the direction of the test.
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01:35Step 1: Write Hypotheses Example 1
Related Practice
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.
Two-tailed test, α=0.02, n=12
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
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
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.
Two-tailed test, α=0.03
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