Domanda del libro di testo
Can a critical value for the chi-square test be negative? Explain.
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Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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TOC.tableOfContents
- 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: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 7, Problema 7.1.30
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.
College Debt According to a recent survey, 14% of adults currently carry student loan debt.
Guida verificata passo dopo passo1
Identify the parameter of interest: The problem is about the proportion of adults who currently carry student loan debt. Let the parameter be denoted as p, where p represents the true proportion of adults with student loan debt.
Translate the claim into a mathematical statement: The claim is that 14% of adults currently carry student loan debt. Mathematically, this is written as p = 0.14.
State the null hypothesis (H₀): The null hypothesis is a statement of no change or no effect. It is typically written as H₀: p = 0.14, which aligns with the claim in this case.
State the alternative hypothesis (H₁): The alternative hypothesis is the complement of the null hypothesis and depends on the context of the problem. If the problem does not specify a direction (greater than or less than), we use a two-tailed test. Thus, H₁: p ≠ 0.14.
Identify which hypothesis represents the claim: Since the claim is that 14% of adults carry student loan debt, and this matches the null hypothesis (H₀: p = 0.14), the null hypothesis represents the claim.
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Null Hypothesis (H0)
The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that assumes any observed effect is due to sampling variability. In this context, it would assert that the proportion of adults with student loan debt is equal to 14%, symbolically represented as H0: p = 0.14.
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Percorso guidato
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. For this scenario, it would claim that the proportion of adults with student loan debt is not equal to 14%, represented as H1: p ≠ 0.14, indicating a potential change in the debt situation.
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Percorso guidato
06:21Step 1: Write Hypotheses
Claim
In hypothesis testing, the claim is the assertion that is being tested, often aligned with the alternative hypothesis. In this case, the claim is that the proportion of adults carrying student loan debt differs from 14%, which is encapsulated in the alternative hypothesis, H1.
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Percorso guidato
01:35Step 1: Write Hypotheses Example 1
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Graphical Analysis In Exercises 9–12, match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning.
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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.
Two-tailed test, n=61,α=0.01
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Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.
Security A campus security department publicizes that at most 25% of applicants become campus security officers.
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Domanda del libro di testo
The mean of a random sample of 18 test scores is x_bar. The standard deviation of the population of all test scores is sigma= 6. Under what condition can you use a z-test to decide whether to reject a claim that the population mean is mu=88?
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