A certain drug is used to treat asthma, In a clinical trial of the drug, 18 of 273 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below. 1-PropZTest prop <0.09 z--1.389447351 p-0.0823483801 p-0.0659340659 n-273 b. What is the test statistic? (Round to two decimal places as needed.) c. What is the P-value? P.value = (Round to four decimal places as needed.) d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. O A. Ho: p=0.09 О В. Но: р<0.09 OC. Ho: p#0.09 O D. Ho: p>0.09 Decide whether to reject the null hypothesis. Choose the correct answer below. O A. Fail to reject the null hypothesis because the P-value is greater than the significance level, a. O B. Reject the null hypothesis because the P-value is greater than the significance level, a. OC. Reject the null hypothesis because the P-value is less than or equal to the significance level, a. O D. Fail to reject the null hypothesis because the P-value sless than or equal to the significance level, a. e. What is the final conclusion? O A. There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches. O B. There is not sufficient evidence warrant rejection of the claim that less than 9% of treated subjects experienced headaches.

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**Title: Statistical Analysis of Headache Incidence in Asthma Drug Trial**

**Background:**
A clinical trial for an asthma treatment evaluated whether less than 9% of treated subjects experienced headaches. In the study, 18 out of 273 subjects reported headaches. Using a normal distribution approximation to the binomial distribution and a 0.01 significance level, the analysis is performed as outlined below.

**Study Section:**

**b. Test Statistic Calculation:**
The Z test statistic is to be calculated and recorded to two decimal places.

**c. P-Value Calculation:**
The P-value will be determined and written out to four decimal places.

**d. Hypothesis Testing:**

**Null Hypothesis (H₀):**
Choices:
- A. H₀: p = 0.09
- B. H₀: p < 0.09
- C. H₀: p ≠ 0.09
- D. H₀: p > 0.09

**Decision Rule:**
Determine whether to reject the null hypothesis:
- Option A: Fail to reject (P-value > α)
- Option B: Reject (P-value > α)
- Option C: Reject (P-value ≤ α)
- Option D: Fail to reject (P-value ≤ α)

**e. Conclusion:**

**Final Conclusion:**
Choose one:
- A. Insufficient evidence to support less than 9% occurrence.
- B. Insufficient evidence to warrant rejection of less than 9% occurrence.

**Graphical Element:**
- **Calculator Display:** 
  - Test: 1-PropZTest
  - Input data: 
    - Proportion being tested: `< 0.09`
    - Test statistic (z): `-1.389447351`
    - P-value: `0.0823438801`
    - Sample proportion (p̂): `0.0659340659`
    - Sample size (n): `273`

This section of the educational resource enables students to engage with hypothesis testing, specifically examining proportion claims in a clinical context. The analysis utilizes statistical tools to draw conclusions based on calculated test statistics and P-values, enhancing understanding of hypothesis testing methods and decision-making processes in real-world research scenarios.
Transcribed Image Text:**Title: Statistical Analysis of Headache Incidence in Asthma Drug Trial** **Background:** A clinical trial for an asthma treatment evaluated whether less than 9% of treated subjects experienced headaches. In the study, 18 out of 273 subjects reported headaches. Using a normal distribution approximation to the binomial distribution and a 0.01 significance level, the analysis is performed as outlined below. **Study Section:** **b. Test Statistic Calculation:** The Z test statistic is to be calculated and recorded to two decimal places. **c. P-Value Calculation:** The P-value will be determined and written out to four decimal places. **d. Hypothesis Testing:** **Null Hypothesis (H₀):** Choices: - A. H₀: p = 0.09 - B. H₀: p < 0.09 - C. H₀: p ≠ 0.09 - D. H₀: p > 0.09 **Decision Rule:** Determine whether to reject the null hypothesis: - Option A: Fail to reject (P-value > α) - Option B: Reject (P-value > α) - Option C: Reject (P-value ≤ α) - Option D: Fail to reject (P-value ≤ α) **e. Conclusion:** **Final Conclusion:** Choose one: - A. Insufficient evidence to support less than 9% occurrence. - B. Insufficient evidence to warrant rejection of less than 9% occurrence. **Graphical Element:** - **Calculator Display:** - Test: 1-PropZTest - Input data: - Proportion being tested: `< 0.09` - Test statistic (z): `-1.389447351` - P-value: `0.0823438801` - Sample proportion (p̂): `0.0659340659` - Sample size (n): `273` This section of the educational resource enables students to engage with hypothesis testing, specifically examining proportion claims in a clinical context. The analysis utilizes statistical tools to draw conclusions based on calculated test statistics and P-values, enhancing understanding of hypothesis testing methods and decision-making processes in real-world research scenarios.
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