er of yes answers on a questionnaire called the Hooked on ne Checklist (HONC). Of teenagers who had tried tobacco, mean HONC score was 3.8 (s=4.4) for the 141 females and s=3.5) for the 178 males. Complete parts a through c below. 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. 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: H₁ H₂. 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.) OCT 29 C Clear all tv Check answer MacBook Air Sal

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### Understanding Teen Addiction to Nicotine

A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The study focused on the response variable, which was the number of "yes" answers on a questionnaire called the Hooked on Nicotine Checklist (HONC).

- **Participants:** 
  - **Females:** 141 with a mean HONC score of 3.8 (standard deviation, \( s = 4.4 \))
  - **Males:** 178 with a mean HONC score of 2.4 (standard deviation, \( s = 3.5 \))

The study involves completing several statistical parts to interpret the data:

#### a. Understanding Standard Error

**Multiple-Choice Options:**

- **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 \( x_1 - x_2 \).
  
- **D.** **(Correct Answer)** The standard error describes the spread of the sampling distribution of \( x_1 - x_2 \).

#### b. Calculating the Test Statistic and P-value

To assess the impact of gender on the mean HONC score, conduct a hypothesis test:

- **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \) 
- **Alternative Hypothesis (Hₐ):** \( \mu_1 \neq \mu_2 \) 

Use a significance level of 0.05 to interpret any gender effects on the mean HONC score. Calculation of the test statistic is required:

\[
\text{The test statistic is } \_\_ \text{ (Round to two decimal places as needed.)}
\]

This exercise encourages students to apply statistical concepts to real-world data, enhancing their understanding of hypothesis testing and gender-related differences in addictive behavior.
Transcribed Image Text:### Understanding Teen Addiction to Nicotine A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The study focused on the response variable, which was the number of "yes" answers on a questionnaire called the Hooked on Nicotine Checklist (HONC). - **Participants:** - **Females:** 141 with a mean HONC score of 3.8 (standard deviation, \( s = 4.4 \)) - **Males:** 178 with a mean HONC score of 2.4 (standard deviation, \( s = 3.5 \)) The study involves completing several statistical parts to interpret the data: #### a. Understanding Standard Error **Multiple-Choice Options:** - **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 \( x_1 - x_2 \). - **D.** **(Correct Answer)** The standard error describes the spread of the sampling distribution of \( x_1 - x_2 \). #### b. Calculating the Test Statistic and P-value To assess the impact of gender on the mean HONC score, conduct a hypothesis test: - **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \) - **Alternative Hypothesis (Hₐ):** \( \mu_1 \neq \mu_2 \) Use a significance level of 0.05 to interpret any gender effects on the mean HONC score. Calculation of the test statistic is required: \[ \text{The test statistic is } \_\_ \text{ (Round to two decimal places as needed.)} \] This exercise encourages students to apply statistical concepts to real-world data, enhancing their understanding of hypothesis testing and gender-related differences in addictive behavior.
Expert Solution
Step 1: Given that

Sample sizes n1=141 ,n2=178

Sample means x1=3.8 ,x2=2.4

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