Questions: Researchers found 400 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the intervention, subjects dropped out of the study. At the end of the study 68 subjects remained in Group 1, 62 in Group 2, and 57 in Group 3. Results as to whether the subject quit smoking entirely are available below. Complete parts (a) through (g). Study Results A. H0: P1=P2=P3 H1: At least one of the proportions is different from the others. B. H0: Quitting and group are independent. H1: Quitting and group are dependent. C. H0: O1=E1 and O2=E2 and O3=E3 H1: O1 ≠ E1 or O2 ≠ E2 or O3 ≠ E3 D. H0: P1=f2=p3 H1: p1 ≠ p2 ≠ p3

Researchers found 400 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the intervention, subjects dropped out of the study. At the end of the study 68 subjects remained in Group 1, 62 in Group 2, and 57 in Group 3. Results as to whether the subject quit smoking entirely are available below. Complete parts (a) through (g). Study Results A. H0: P1=P2=P3 H1: At least one of the proportions is different from the others. B. H0: Quitting and group are independent. H1: Quitting and group are dependent. C. H0: O1=E1 and O2=E2 and O3=E3 H1: O1 ≠ E1 or O2 ≠ E2 or O3 ≠ E3 D. H0: P1=f2=p3 H1: p1 ≠ p2 ≠ p3
Transcript text: Researchers found 400 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the intervention, subjects dropped out of the study. At the end of the study 68 subjects remained in Group 1, 62 in Group 2, and 57 in Group 3. Results as to whether the subject quit smoking entirely are available below. Complete parts (a) through (g). Study Results A. $\mathrm{H}_{0}: \mathrm{P}_{1}=\mathrm{P}_{2}=\mathrm{p}_{3}$ $\mathrm{H}_{1}$ : At least one of the proportions is different from the others. B. $\mathrm{H}_{0}$ : Quitting and group are independent. $H_{1}$ : Quitting and group are dependent. C. $\mathrm{H}_{0}: \mathrm{O}_{1}=\mathrm{E}_{1}$ and $\mathrm{O}_{2}=\mathrm{E}_{2}$ and $\mathrm{O}_{3}=\mathrm{E}_{3}$ $\mathrm{H}_{1}: \mathrm{O}_{1} \neq \mathrm{E}_{1}$ or $\mathrm{O}_{2} \neq \mathrm{E}_{2}$ or $\mathrm{O}_{3} \neq \mathrm{E}_{3}$ D. $H_{0}: P_{1}=f_{2}=p_{3}$ $H_{1}: p_{1} \neq p_{2} \neq p_{3}$
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Solution

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Solution Steps

To state the null and alternative hypotheses for this study, we need to determine the relationship between the treatment groups and the outcome of quitting smoking. The null hypothesis typically states that there is no effect or no difference, while the alternative hypothesis states that there is an effect or a difference.

Solution Approach
  • The null hypothesis (H0) would state that the proportions of subjects who quit smoking are the same across all three groups.
  • The alternative hypothesis (H1) would state that at least one of the proportions is different from the others.
Step 1: Define the Null and Alternative Hypotheses

In this study, we are interested in the relationship between the treatment groups and the outcome of quitting smoking. The hypotheses can be defined as follows:

  • Null Hypothesis (\(H_0\)): \(P_1 = P_2 = P_3\)
    This states that the proportions of subjects who quit smoking are equal across all three treatment groups.

  • Alternative Hypothesis (\(H_1\)): At least one of the proportions is different from the others.
    This indicates that there is a significant difference in the quitting rates among the treatment groups.

Final Answer

The hypotheses for the study are:

  • Null Hypothesis (\(H_0\)): \(P_1 = P_2 = P_3\)
  • Alternative Hypothesis (\(H_1\): At least one of the proportions is different from the others.

Thus, the final answer is: \[ \boxed{H_0: P_1 = P_2 = P_3, \quad H_1: \text{At least one of the proportions is different}} \]

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