20.24 (EX) Drug testing in schools, continued 1/4: In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High School tested athletes at random and Warrenton High School did not. In a confidential survey, 7 of 135 athletes at Wahtonka and 27 of 141 athletes at Warrenton said they were using drugs. Regard these athletes as SRSS from the populations of athletes at similar schools with and without drug testing. Do the data give good reason to think that drug use among athletes is lower in schools that test for drugs? Take p₁ and p2 to be the proportions of athletes that use drugs, in all high-schools without drug testing and with drug testing, respectively. The hypotheses to be tested are: O Ho: P1 O Ho: P1 O Ho: P1 O Ho: P1 P2, H₂: P₁ P2 P2, H₂: P₁ P2, Ha: P1 P2, H₂: P1 P2 P2 P2

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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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 Find the z-test statistic for the hypothesis. Round your answer to two decimal points

The P-value is?

### Drug Testing in Schools: Analyzing the Impact on Drug Use Among Athletes

**Context:**
In 2002, the Supreme Court ruled that schools could mandate random drug tests for students in competitive after-school activities, like athletics. This raised the question: Do drug tests effectively reduce illegal drug use among students? A study was conducted to evaluate this by comparing two high schools in Oregon: Wahtonka High School and Warrenton High School. Wahtonka implemented random drug testing for athletes, whereas Warrenton did not.

**Study Details:**
- **Wahtonka High School:** Out of 135 athletes surveyed, 7 admitted to using drugs.
- **Warrenton High School:** Out of 141 athletes surveyed, 27 admitted to using drugs.

**Objective:**
To determine if drug use among athletes is significantly lower in schools that conduct drug testing.

**Hypotheses:**
- Define \( p_1 \) as the proportion of athletes using drugs in schools without drug testing.
- Define \( p_2 \) as the proportion of athletes using drugs in schools with drug testing.

The hypotheses to be tested are:
1. \( H_0: p_1 = p_2 \), \( H_a: p_1 > p_2 \)
2. \( H_0: p_1 = p_2 \), \( H_a: p_1 \neq p_2 \)
3. \( H_0: p_1 = p_2 \), \( H_a: p_1 < p_2 \)
4. \( H_0: p_1 \neq p_2 \), \( p_1 = p_2 \)

#### Explanation:
The study aims to assess whether the implementation of drug tests in schools leads to a statistically significant reduction in drug use among athletes. By analyzing survey data and conducting hypothesis testing, the study provides insights into the effectiveness of drug testing programs in reducing illegal drug use.
Transcribed Image Text:### Drug Testing in Schools: Analyzing the Impact on Drug Use Among Athletes **Context:** In 2002, the Supreme Court ruled that schools could mandate random drug tests for students in competitive after-school activities, like athletics. This raised the question: Do drug tests effectively reduce illegal drug use among students? A study was conducted to evaluate this by comparing two high schools in Oregon: Wahtonka High School and Warrenton High School. Wahtonka implemented random drug testing for athletes, whereas Warrenton did not. **Study Details:** - **Wahtonka High School:** Out of 135 athletes surveyed, 7 admitted to using drugs. - **Warrenton High School:** Out of 141 athletes surveyed, 27 admitted to using drugs. **Objective:** To determine if drug use among athletes is significantly lower in schools that conduct drug testing. **Hypotheses:** - Define \( p_1 \) as the proportion of athletes using drugs in schools without drug testing. - Define \( p_2 \) as the proportion of athletes using drugs in schools with drug testing. The hypotheses to be tested are: 1. \( H_0: p_1 = p_2 \), \( H_a: p_1 > p_2 \) 2. \( H_0: p_1 = p_2 \), \( H_a: p_1 \neq p_2 \) 3. \( H_0: p_1 = p_2 \), \( H_a: p_1 < p_2 \) 4. \( H_0: p_1 \neq p_2 \), \( p_1 = p_2 \) #### Explanation: The study aims to assess whether the implementation of drug tests in schools leads to a statistically significant reduction in drug use among athletes. By analyzing survey data and conducting hypothesis testing, the study provides insights into the effectiveness of drug testing programs in reducing illegal drug use.
**Exercise 20.24 (EX) Drug Testing in Schools, Continued 4/4:**

**Instruction:** Determine which of the following statements best describes your conclusion.

1. O There is good evidence that drug use among athletes is lower in schools that test for drugs.

2. O There is not enough evidence to reject the null hypothesis.

3. O There is good evidence that drug use among athletes is higher in schools that test for drugs.

4. O There is good evidence that drug use among athletes is different between schools that test for drugs and schools that don't.

**Explanation:** The options provided require the selection of the statement that best reflects the findings from a hypothetical or real study on drug testing effectiveness in schools. Each choice offers a different conclusion about the relationship between drug testing and drug use among athletes.
Transcribed Image Text:**Exercise 20.24 (EX) Drug Testing in Schools, Continued 4/4:** **Instruction:** Determine which of the following statements best describes your conclusion. 1. O There is good evidence that drug use among athletes is lower in schools that test for drugs. 2. O There is not enough evidence to reject the null hypothesis. 3. O There is good evidence that drug use among athletes is higher in schools that test for drugs. 4. O There is good evidence that drug use among athletes is different between schools that test for drugs and schools that don't. **Explanation:** The options provided require the selection of the statement that best reflects the findings from a hypothetical or real study on drug testing effectiveness in schools. Each choice offers a different conclusion about the relationship between drug testing and drug use among athletes.
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