Textbook Question
In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.
Claim: μ≥8000; α=0.01. Sample statistics: x_bar=77,000, s=450, n=25
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 7.1.28
Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
Attendance An amusement park claims that the mean daily attendance at the park is at least 20,000 people.
Verified step by step guidance1
Understand the problem: The amusement park claims that the mean daily attendance is at least 20,000 people. This is the claim we need to translate into a mathematical statement and then formulate the null and alternative hypotheses.
Express the claim mathematically: The claim 'at least 20,000 people' means the mean daily attendance (denoted as μ) is greater than or equal to 20,000. Mathematically, this is written as μ ≥ 20,000.
Define the null hypothesis (H₀): The null hypothesis always includes equality. Since the claim involves 'at least,' the null hypothesis is H₀: μ ≥ 20,000.
Define the alternative hypothesis (H₁): The alternative hypothesis is the complement of the null hypothesis. Since the null states 'μ ≥ 20,000,' the alternative hypothesis is H₁: μ < 20,000.
Identify the claim: The claim is represented by the null hypothesis (H₀: μ ≥ 20,000) because it directly aligns with the amusement park's statement.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis
The null hypothesis (H0) 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 daily attendance at the amusement park is 20,000 or more, which is the claim being tested.
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06:21
Step 1: Write Hypotheses
Alternative Hypothesis
The alternative hypothesis (H1) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, the alternative hypothesis would state that the mean daily attendance is less than 20,000, representing the possibility that the park's claim is not true.
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06:21Step 1: Write Hypotheses
Mathematical Representation of Hypotheses
Mathematical representation of hypotheses involves formulating the null and alternative hypotheses in a precise manner using symbols. For this example, the null hypothesis can be expressed as H0: μ ≥ 20,000, while the alternative hypothesis can be expressed as H1: μ < 20,000, where μ represents the mean daily attendance.
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06:21Step 1: Write Hypotheses
Related Practice
Textbook Question
Graphical Analysis In Exercises 9–12, match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning.
z = -2.37
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.
MCAT Scores A random sample of 100 medical school applicants at a university has a mean total score of 505 on the MCAT. According to a report, the mean total score for the school’s applicants is more than 503. Assume the population standard deviation is 10.6. At alpha=0.01, is there enough evidence to support the report’s claim?
1
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Textbook Question
How do the requirements for a chi-square test for a variance or standard deviation differ from a z-test or a t-test for a mean?
Textbook Question
In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.
Left-tailed test, n=7,α=0.01
Textbook Question
Hypothesis Testing Using Rejection Regions In Exercises 19–26, (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 t, (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.
Annual Salary An employment information service claims the mean annual salary for senior level statisticians is more than \(124,000. The annual salaries (in dollars) for a random sample of 12 senior level statisticians are shown in the table at the left. At α=0.01, is there enough evidence to support the claim that the mean salary is more than \)124,000?