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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 7 - Hypothesis Testing with One Sample문제 7.1.21
7장, 문제 7.1.21

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.


Ha: μ ≤ 8.0
H0: μ > 8.0

검증된 단계별 안내
1
Step 1: Understand the null hypothesis (H₀) and the alternative hypothesis (Hₐ). In this problem, H₀: μ > 8.0 and Hₐ: μ ≤ 8.0. The null hypothesis represents the default assumption, while the alternative hypothesis represents the claim being tested.
Step 2: Identify the direction of the inequality in the alternative hypothesis (Hₐ). Here, Hₐ: μ ≤ 8.0 indicates that the mean (μ) is less than or equal to 8.0.
Step 3: Recall that the direction of the test is determined by the alternative hypothesis. Specifically: (a) If Hₐ uses '<', it is a left-tailed test. (b) If Hₐ uses '>', it is a right-tailed test. (c) If Hₐ uses '≠', it is a two-tailed test.
Step 4: Since Hₐ: μ ≤ 8.0 includes the '≤' symbol, this implies a left-tailed test because we are testing for values less than or equal to a specific value (8.0).
Step 5: Conclude that the hypothesis test is left-tailed based on the direction of the inequality in the alternative hypothesis.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents no effect or status quo, and the alternative hypothesis (Ha), which represents the effect or difference we suspect. The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Types of Hypothesis Tests

Hypothesis tests can be classified as left-tailed, right-tailed, or two-tailed based on the direction of the alternative hypothesis. A left-tailed test is used when Ha indicates that the parameter is less than a certain value, while a right-tailed test is used when Ha indicates it is greater. A two-tailed test is employed when Ha suggests that the parameter is simply different from a certain value, without specifying a direction.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Interpreting Hypotheses

In the given hypotheses, Ha: μ ≤ 8.0 suggests that the population mean is less than or equal to 8.0, while H0: μ > 8.0 indicates that the mean is greater than 8.0. This setup implies a left-tailed test, as we are interested in determining if the mean is significantly less than 8.0. Understanding the direction of the hypotheses is crucial for selecting the appropriate statistical test and interpreting the results.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses
관련 실천
교과서 질문

Hypothesis Testing Using Rejection Regions In Exercises 23–30, (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 X^2, (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.


Salaries The annual salaries (in dollars) of 12 randomly chosen nursing supervisors are shown in the table at the left. At α=0.10, is there enough evidence to reject the claim that the standard deviation of the annual salaries is \$18,630?


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교과서 질문

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

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교과서 질문

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

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교과서 질문

Hypothesis Testing Using Rejection Region(s) In Exercises 39–44, (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.


[APPLET] Fluorescent Lamps A compact fluorescent lamp (CFL) bulb manufacturer guarantees that the mean life of a CFL bulb is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of 32 CFL bulbs. The results (in hours) are listed. Assume the population standard deviation is 1850 hours. At alpha=0.11, do you have enough evidence to reject the manufacturer’s claim?


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교과서 질문

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.


Lead Levels As part of your work for an environmental awareness group, you want to test a claim that the mean amount of lead in the air in U.S. cities is less than 0.032 microgram per cubic meter. You find that the mean amount of lead in the air for a random sample of 56 U.S. cities is 0.021 microgram per cubic meter and the standard deviation is 0.034 microgram per cubic meter. At α=0.01, can you support the claim?

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교과서 질문

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.


To support a claim, state it so that it becomes the null hypothesis.

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