A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The response variable was the number of yes answers on a questionnaire called the Hooked on Nicotine Checklist (HONC). Of teenagers who had tried tobacco, the mean HONC score was 3.8 (s = 4.4) for the 141 females and 2.4 (s = 3.5) for the 178 males. Complete parts a through c below. ... a. Find the standard error comparing the sample means. Interpret. The standard error is se= 0.4540. (Round to four decimal places as needed.) What does the standard error indicate? OA. The standard error is the standard deviation of the sample for this study. OB. The standard error is the difference in standard deviations for the two populations. OC. The standard error is the standard deviation of the difference between x₁-x₂. D. The standard error describes the spread of the sampling distribution of x₁-x₂. b. Find the test statistic and P-value for Ho: H₁ H₂ and H₂: µ₁ ‡µ₂. Interpret, and explain what (if any) effect gender has on the mean HONC score. Use the significance level 0.05. The test statistic is (Round to two decimal places as needed.)

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### Study on Teen Nicotine Addiction

A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The response variable was the number of "yes" answers on a questionnaire called the Hooked on Nicotine Checklist (HONC). Among teenagers who had tried tobacco, the mean HONC score was 3.8 (standard deviation = 4.4) for 141 females and 2.4 (standard deviation = 3.5) for 178 males. The tasks below were part of the study analysis:

#### Part a: Standard Error

- **Find the standard error comparing the sample means. Interpret.**

  The standard error is \( \text{se} = 0.4540 \).
  
  *(Rounded to four decimal places as needed.)*

- **What does the standard error indicate?**

  Choices:
  - A: The standard error is the standard deviation of the sample for this study.
  - B: The standard error is the difference in standard deviations for the two populations.
  - C: The standard error is the standard deviation of the difference between \( \bar{x}_1 - \bar{x}_2 \).
  - **D (Correct):** The standard error describes the spread of the sampling distribution of \( \bar{x}_1 - \bar{x}_2 \).

#### Part b: Test Statistic and P-value

- **Find the test statistic and P-value for \( H_0: \mu_1 = \mu_2 \) and \( H_a: \mu_1 \neq \mu_2 \).**

  - Interpret, and explain what (if any) effect gender has on the mean HONC score. Use a significance level of 0.05.

  - The test statistic is \( \_\_\_ \).

  *(Round to two decimal places as needed.)*

### Note
The task involved filling in a blank test statistic value, which requires further calculation not provided in the image.
Transcribed Image Text:### Study on Teen Nicotine Addiction A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The response variable was the number of "yes" answers on a questionnaire called the Hooked on Nicotine Checklist (HONC). Among teenagers who had tried tobacco, the mean HONC score was 3.8 (standard deviation = 4.4) for 141 females and 2.4 (standard deviation = 3.5) for 178 males. The tasks below were part of the study analysis: #### Part a: Standard Error - **Find the standard error comparing the sample means. Interpret.** The standard error is \( \text{se} = 0.4540 \). *(Rounded to four decimal places as needed.)* - **What does the standard error indicate?** Choices: - A: The standard error is the standard deviation of the sample for this study. - B: The standard error is the difference in standard deviations for the two populations. - C: The standard error is the standard deviation of the difference between \( \bar{x}_1 - \bar{x}_2 \). - **D (Correct):** The standard error describes the spread of the sampling distribution of \( \bar{x}_1 - \bar{x}_2 \). #### Part b: Test Statistic and P-value - **Find the test statistic and P-value for \( H_0: \mu_1 = \mu_2 \) and \( H_a: \mu_1 \neq \mu_2 \).** - Interpret, and explain what (if any) effect gender has on the mean HONC score. Use a significance level of 0.05. - The test statistic is \( \_\_\_ \). *(Round to two decimal places as needed.)* ### Note The task involved filling in a blank test statistic value, which requires further calculation not provided in the image.
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