Textbook Question
Explain how to find critical values for a t-distribution.
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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 7.1.6
True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A statistical hypothesis is a statement about a sample.
Verified step by step guidance1
Understand the definition of a statistical hypothesis: A statistical hypothesis is a statement or claim about a population parameter (e.g., population mean, proportion, variance) rather than a sample.
Analyze the given statement: The problem claims that a statistical hypothesis is a statement about a sample.
Compare the definition with the statement: Since a statistical hypothesis pertains to the population and not the sample, the given statement is false.
Rewrite the statement to make it true: A statistical hypothesis is a statement about a population parameter, not a sample.
Conclude the reasoning: The corrected statement aligns with the definition of a statistical hypothesis, ensuring clarity and accuracy.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Statistical Hypothesis
A statistical hypothesis is a specific claim or assertion about a population parameter, such as a mean or proportion. It can be tested using statistical methods to determine its validity. Hypotheses are typically formulated in pairs: the null hypothesis (H0), which represents no effect or no difference, and the alternative hypothesis (H1), which represents the effect or difference being tested.
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06:34
Step 2: Calculate Test Statistic
Population vs. Sample
In statistics, a population refers to the entire group of individuals or instances about which we seek to draw conclusions, while a sample is a subset of that population selected for analysis. Hypotheses are generally concerned with population parameters, not sample statistics, as they aim to infer characteristics of the whole population based on the sample data.
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True/False Statements in Statistics
In statistical exercises, determining the truth value of a statement often involves understanding the definitions and relationships between concepts. A statement can be true or false based on established statistical principles, and if false, it can be rewritten to reflect the correct understanding, such as clarifying that a statistical hypothesis pertains to a population rather than a sample.
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06:34Step 2: Calculate Test Statistic
Related Practice
Textbook Question
Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
Ha: μ ≥ 5.2
H0: μ < 5.2
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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.
Right-tailed test, α=0.02, n=63
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Textbook Question
Hypothesis Testing Using Rejection Regions In Exercises 7–12, (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 z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Working Students An education researcher claims that 65% of full-time college students work year-round. In a random sample of 105 college students, 66 say they work year-round. At α=0.10, is there enough evidence to reject the researcher’s claim?
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Textbook Question
Hypothesis Testing Using a P-Value In Exercises 33–38,
a. identify the claim and state and .
b. find the standardized test statistic z.
c. find the corresponding P-value.
d. decide whether to reject or fail to reject the null hypothesis.
e. interpret the decision in the context of the original claim.
Sprinkler Systems A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°F. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133°F. Assume the population standard deviation is 3.3°F. At alpha=0.10, do you have enough evidence to reject the manufacturer’s claim?
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Textbook Question
Faculty Classroom Hours The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table at the left. At α=0.01, can you reject the dean’s claim?
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