2. In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from "High Dose Nicotine Patch Therapy," by Dale et al.., Journal of the American Medical Association, Vol. 274, No. 17). We want to use a 0.05 sig- nificance level to test the claim that among smokers who try

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The question I need answered is question 2, parts a-i.

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### Statistical Analysis of Nicotine Patch Therapy

In a study examining the effectiveness of nicotine patch therapy, it was claimed that the majority of smokers who attempt to quit end up smoking again a year after the treatment. Below are questions and concepts to guide an analysis of this claim:

#### a. What is the null hypothesis?
- The null hypothesis typically states that there is no effect or no difference. In this context, it might propose that the proportion of smokers who continue smoking after a year is equal to or less than half.

#### b. What is the alternative hypothesis?
- The alternative hypothesis suggests a difference or effect exists. Here, it could claim that the majority (more than half) continue smoking after a year despite the therapy.

#### c. What is the value of the standard score for the sample proportion?
- This refers to the z-score calculated for the sample proportion, indicating how many standard deviations the observed proportion is from the hypothesized population proportion under the null hypothesis.

#### d. What is the critical value?
- The critical value determines the cutoff point(s) for rejecting the null hypothesis. It is based on the chosen significance level (e.g., 0.05) and the directionality of the test (one-tailed or two-tailed).

#### e. What is the P-value?
- The P-value helps to measure the strength of the evidence against the null hypothesis. A smaller P-value indicates stronger evidence to reject the null hypothesis.

#### f. What do you conclude?
- A conclusion should address whether the evidence is sufficient to reject the null hypothesis, specifically in the context of whether the majority of smokers remain smoking a year post-therapy.

#### g. Describe a Type I error for this test.
- A Type I error occurs when the null hypothesis is incorrectly rejected when it is true. In this case, it would mean concluding that the majority of smokers continue smoking when they actually don't.

#### h. Describe a Type II error for this test.
- A Type II error happens when the null hypothesis is not rejected when it is false. Here, it would suggest failing to identify that the therapy is ineffective when, in reality, it is.

#### i. What is the P-value if the claim is modified to state that the proportion is equal to 0.5?
- This asks for a recalculation of the P-value when the null hypothesis is adjusted to test whether the proportion of smokers who continue is exactly 50%.

These questions provide a framework for analyzing
Transcribed Image Text:### Statistical Analysis of Nicotine Patch Therapy In a study examining the effectiveness of nicotine patch therapy, it was claimed that the majority of smokers who attempt to quit end up smoking again a year after the treatment. Below are questions and concepts to guide an analysis of this claim: #### a. What is the null hypothesis? - The null hypothesis typically states that there is no effect or no difference. In this context, it might propose that the proportion of smokers who continue smoking after a year is equal to or less than half. #### b. What is the alternative hypothesis? - The alternative hypothesis suggests a difference or effect exists. Here, it could claim that the majority (more than half) continue smoking after a year despite the therapy. #### c. What is the value of the standard score for the sample proportion? - This refers to the z-score calculated for the sample proportion, indicating how many standard deviations the observed proportion is from the hypothesized population proportion under the null hypothesis. #### d. What is the critical value? - The critical value determines the cutoff point(s) for rejecting the null hypothesis. It is based on the chosen significance level (e.g., 0.05) and the directionality of the test (one-tailed or two-tailed). #### e. What is the P-value? - The P-value helps to measure the strength of the evidence against the null hypothesis. A smaller P-value indicates stronger evidence to reject the null hypothesis. #### f. What do you conclude? - A conclusion should address whether the evidence is sufficient to reject the null hypothesis, specifically in the context of whether the majority of smokers remain smoking a year post-therapy. #### g. Describe a Type I error for this test. - A Type I error occurs when the null hypothesis is incorrectly rejected when it is true. In this case, it would mean concluding that the majority of smokers continue smoking when they actually don't. #### h. Describe a Type II error for this test. - A Type II error happens when the null hypothesis is not rejected when it is false. Here, it would suggest failing to identify that the therapy is ineffective when, in reality, it is. #### i. What is the P-value if the claim is modified to state that the proportion is equal to 0.5? - This asks for a recalculation of the P-value when the null hypothesis is adjusted to test whether the proportion of smokers who continue is exactly 50%. These questions provide a framework for analyzing
In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from "High Dose Nicotine Patch Therapy," by Dale et al., *Journal of the American Medical Association*, Vol. 274, No. 17). We want to use a 0.05 significance level to test the claim that among smokers who try

---

Page Number: 338  
Section Title: Hypothesis Testing

(Note: The text cuts off at "among smokers who try", indicating that there might be additional context or findings on the hypothesis testing process in the study.)
Transcribed Image Text:In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from "High Dose Nicotine Patch Therapy," by Dale et al., *Journal of the American Medical Association*, Vol. 274, No. 17). We want to use a 0.05 significance level to test the claim that among smokers who try --- Page Number: 338 Section Title: Hypothesis Testing (Note: The text cuts off at "among smokers who try", indicating that there might be additional context or findings on the hypothesis testing process in the study.)
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