which method would help smokers quit smoking. He divided a group of 183 sm patch, Group 2 is given oral medication, and Group 3.has no intervention. The re Test the researcher's claim using a significance level of a = 0.05. Group 2 Group 3 54 51 9 4 ternative hypotheses. 5 for helping people quit smoking are the same. 5 for helping people quit smoking follow a different distribution. = for helping people quit smoking are independent. 5 for helping people quit smoking are dependent. tic. Round your answer to two decimal places. Round your answer to four decimal places. null hypothesis. ypothesis. icient evidence to support the claim that the methods for helping people quit smoking an nt evidence to support the claim that the methods for helping people quit smoking are structor

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### Evaluating Methods to Help Smokers Quit Smoking

A researcher wanted to determine which method would help smokers quit smoking. He divided a group of 183 smokers into three groups:

- **Group 1**: Given a patch
- **Group 2**: Given oral medication
- **Group 3**: No intervention (Control Group)

The results of the study are shown in the table below. The researcher's claim is tested using a significance level of \( \alpha = 0.05 \).

#### Table: Results of the Study

|                | Group 1 | Group 2 | Group 3 |
|:--------------:|:-------:|:-------:|:-------:|
| **Did Not Quit** |   52   |   54   |   51   |
|    **Quit**      |   13   |   9    |    4   |

*Source: Harris Poll*

#### Hypotheses

a. **Determine the null and alternative hypotheses.**

- **Option 1:**
  - \( H_0 \): The methods for helping people quit smoking are the same.
  - \( H_a \): The methods for helping people quit smoking follow a different distribution.
- **Option 2:**
  - \( H_0 \): The methods for helping people quit smoking are independent.
  - \( H_a \): The methods for helping people quit smoking are dependent.

[Select the appropriate hypotheses based on the study's context.]

#### Statistical Analysis

b. **Determine the test statistic. Round your answer to two decimal places.**

\[ \chi^2 = \_ \_ . \_ \_ \]

c. **Determine the p-value. Round your answer to four decimal places.**

\[ \text{p-value} = \_ . \_ \_ \_ \_ \]

#### Decision Making

d. **Make a decision.**

- Fail to reject the null hypothesis.
- Reject the null hypothesis.

[Select the appropriate decision based on the calculated test statistic and p-value.]

e. **Make a conclusion.**

- There is not sufficient evidence to support the claim that the methods for helping people quit smoking are different.
- There is sufficient evidence to support the claim that the methods for helping people quit smoking are different.

[Select the appropriate conclusion based on the decision from part (d).]

#### Explanation of Graphs or Diagrams

-
Transcribed Image Text:### Evaluating Methods to Help Smokers Quit Smoking A researcher wanted to determine which method would help smokers quit smoking. He divided a group of 183 smokers into three groups: - **Group 1**: Given a patch - **Group 2**: Given oral medication - **Group 3**: No intervention (Control Group) The results of the study are shown in the table below. The researcher's claim is tested using a significance level of \( \alpha = 0.05 \). #### Table: Results of the Study | | Group 1 | Group 2 | Group 3 | |:--------------:|:-------:|:-------:|:-------:| | **Did Not Quit** | 52 | 54 | 51 | | **Quit** | 13 | 9 | 4 | *Source: Harris Poll* #### Hypotheses a. **Determine the null and alternative hypotheses.** - **Option 1:** - \( H_0 \): The methods for helping people quit smoking are the same. - \( H_a \): The methods for helping people quit smoking follow a different distribution. - **Option 2:** - \( H_0 \): The methods for helping people quit smoking are independent. - \( H_a \): The methods for helping people quit smoking are dependent. [Select the appropriate hypotheses based on the study's context.] #### Statistical Analysis b. **Determine the test statistic. Round your answer to two decimal places.** \[ \chi^2 = \_ \_ . \_ \_ \] c. **Determine the p-value. Round your answer to four decimal places.** \[ \text{p-value} = \_ . \_ \_ \_ \_ \] #### Decision Making d. **Make a decision.** - Fail to reject the null hypothesis. - Reject the null hypothesis. [Select the appropriate decision based on the calculated test statistic and p-value.] e. **Make a conclusion.** - There is not sufficient evidence to support the claim that the methods for helping people quit smoking are different. - There is sufficient evidence to support the claim that the methods for helping people quit smoking are different. [Select the appropriate conclusion based on the decision from part (d).] #### Explanation of Graphs or Diagrams -
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