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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 9 - Inferences from Two Samples문제 9.1.3a
9장, 문제 9.1.3a

Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.


a. Identify the null hypothesis and the alternative hypothesis.

검증된 단계별 안내
1
Step 1: Understand the context of hypothesis testing. In hypothesis testing, we aim to make a decision about a population parameter based on sample data. The null hypothesis (H₀) represents the default assumption or status quo, while the alternative hypothesis (H₁) represents the claim we are testing against the null hypothesis.
Step 2: Identify the population parameter or claim being tested in Exercise 1.a. Carefully read the description of Exercise 1.a to determine what is being tested (e.g., mean, proportion, variance, etc.). This will help in formulating the hypotheses.
Step 3: Formulate the null hypothesis (H₀). The null hypothesis typically states that there is no effect, no difference, or that the population parameter equals a specific value. For example, H₀: μ = μ₀ (where μ₀ is the hypothesized population mean).
Step 4: Formulate the alternative hypothesis (H₁). The alternative hypothesis represents the claim being tested and is often expressed as a statement of inequality (e.g., H₁: μ ≠ μ₀, H₁: μ > μ₀, or H₁: μ < μ₀). The direction of the inequality depends on the context of the problem.
Step 5: Verify the hypotheses. Ensure that the null and alternative hypotheses are mutually exclusive and collectively exhaustive, meaning they cover all possible outcomes of the test. This ensures the hypothesis test is properly set up.

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주요 개념

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Null Hypothesis

The null hypothesis (H0) is a statement that indicates no effect or no difference in a statistical test. It serves as a default position that assumes any observed effect is due to sampling variability. Researchers aim to gather evidence to reject the null hypothesis in favor of the alternative hypothesis.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Alternative Hypothesis

The alternative hypothesis (H1 or Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents the researcher's claim or the outcome they are trying to prove. The alternative hypothesis is what researchers hope to support through their statistical analysis.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating both a null and an alternative hypothesis, then using sample data to determine whether to reject the null hypothesis. The process includes calculating a test statistic and comparing it to a critical value or p-value to assess significance.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses
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Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed (based on data from “Who Wants Airbags?” by Meyer and Finney, Chance, Vol. 18, No. 2). We want to use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.


a. Test the claim using a hypothesis test.

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교과서 질문

Independent Samples Which of the following involve independent samples?


a. Data Set 4 “Measured and Reported” includes measured heights matched with the heights that were reported when the subjects were asked for those values.


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교과서 질문

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)


Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Higher scores correspond to more creativity. The researchers make the claim that “blue enhances performance on a creative task.”


a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task.


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교과서 질문

In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.


Measured and Reported Weights Listed below are measured and reported weights (lb) of random female subjects (from Data Set 4 “Measured and Reported” in Appendix B).


a. Use a 0.05 significance level to test the claim that for females, the measured weights tend to be higher than the reported weights.


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교과서 질문

Confidence Interval Assume that we want to use the sample data in Exercise 1 for constructing a confidence interval to be used for testing the given claim.


a. What is the confidence level that should be used for the confidence interval?


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교과서 질문

Count Five Test for Comparing Variation in Two Populations Repeat Exercise 16 “Blanking Out on Tests,” but instead of using the F test, use the following procedure for the “count five” test of equal variations (which is not as complicated as it might appear).

a. For each value x in the first sample, find the absolute deviation |x-x_bar| then sort the absolute deviation values. Do the same for the second sample.

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