9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

2:21 minutes

Problem 6.R.6b

Textbook Question

Smoking Cessation Programs

b. Does the difference between the success rate of the sustained care program and the standard care program appear to have practical significance?

Verified step by step guidance

Identify the success rates for both the sustained care program and the standard care program. Denote these as p1 (sustained care) and p2 (standard care).

Calculate the difference in success rates: Δp = p1 - p2. This will give the observed difference in proportions.

Assess whether the observed difference Δp is large enough to be considered practically significant. Practical significance depends on the context and whether the difference is meaningful in real-world terms (e.g., does it justify additional costs or resources?).

Consider the sample sizes and variability in the data. Larger sample sizes reduce variability and make smaller differences more reliable, which can influence practical significance.

If needed, consult a predefined threshold for practical significance (e.g., a minimum difference that stakeholders consider meaningful) to determine if the observed difference meets this criterion.

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Key Concepts

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

Practical Significance

Practical significance refers to the real-world relevance or importance of a statistical finding. While a result may be statistically significant, indicating that it is unlikely to have occurred by chance, practical significance assesses whether the effect size is large enough to be meaningful in a practical context. In the case of smoking cessation programs, this would involve evaluating whether the difference in success rates translates into a noticeable improvement in outcomes for participants.

Effect Size

Effect size is a quantitative measure that reflects the magnitude of a phenomenon or the strength of a relationship between variables. In the context of comparing success rates of smoking cessation programs, effect size helps to determine how substantial the difference is between the sustained care and standard care programs. A larger effect size indicates a more significant difference, which can inform decisions about which program to implement.

Statistical Significance

Statistical significance assesses whether the observed differences in data are likely due to chance or represent a true effect. It is typically determined using a p-value, where a p-value less than a predetermined threshold (commonly 0.05) suggests that the results are statistically significant. Understanding statistical significance is crucial when evaluating the success rates of different smoking cessation programs, as it helps to validate the findings before considering their practical implications.

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Textbook Question

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Textbook Question

Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program. Test the claim using a hypothesis test.

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Smoking Cessation Programsb. Does the difference between the success rate of the sustained care program and the standard care program appear to have practical significance?

Key Concepts

Practical Significance

Effect Size

Statistical Significance

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Smoking Cessation Programs

b. Does the difference between the success rate of the sustained care program and the standard care program appear to have practical significance?