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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 9 - Inferences from Two SamplesProblem 9.1.3b
Chapter 9, Problem 9.1.3b

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


b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim?

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1
Identify the null hypothesis (H₀) and the alternative hypothesis (H₁) for the test. The null hypothesis typically represents the default or no-effect assumption, while the alternative hypothesis represents the claim being tested.
Recall the significance level (α) for the hypothesis test. If not explicitly stated, a common default value is α = 0.05.
Compare the reported P-value (less than 0.001) to the significance level (α). If the P-value is less than α, reject the null hypothesis (H₀).
Since the P-value is less than 0.001, it is much smaller than typical significance levels like 0.05 or 0.01. This indicates strong evidence against the null hypothesis (H₀).
Conclude that the original claim, represented by the alternative hypothesis (H₁), is supported by the data. State that there is strong evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a default position, and the alternative hypothesis (H1), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.
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Step 1: Write Hypotheses

P-value

The P-value is a measure that helps determine the strength of the evidence against the null hypothesis. It represents the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, with common thresholds being 0.05, 0.01, and 0.001.
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Step 3: Get P-Value

Statistical Significance

Statistical significance refers to the likelihood that a relationship observed in data is not due to random chance. When the P-value is less than a predetermined significance level (often 0.05), the results are considered statistically significant, leading to the rejection of the null hypothesis. In this case, a P-value less than 0.001 suggests very strong evidence against the null hypothesis, indicating that the original claim is likely true.
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Parameters vs. Statistics
Related Practice
Textbook Question

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.”


b. Construct the confidence interval appropriate for the hypothesis test in part (a). What is it about the confidence interval that causes us to reach the same conclusion from part (a)?


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Textbook Question

F Test Statistic


b. Can the F test statistic ever be a negative number?


Textbook Question

Friday the 13th Refer to the sample data from Exercise 1.


b. In general, what does ud represent?

Textbook Question

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)


Magnet Treatment of Pain People spend around \$5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels.


b. Construct the confidence interval appropriate for the hypothesis test in part (a).


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Textbook Question

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.


Do Men Talk Less than Women? Listed below are word counts of males and females in couple relationships (from Data Set 14 “Word Counts” in Appendix B).


b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?


Textbook Question

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.


b. Test the claim by constructing an appropriate confidence interval.