Two-tailed test b. What is the test statistic? z = - 3.22 (Round to two decimal places as needed.) c. What is the P-value? P-value = [ (Round to four decimal places as needed.)

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A certain drug is used to treat asthma. In a clinical trial of the drug, 15 of 293 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 11% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below.

- Two-tailed test

**b. What is the test statistic?**

\( z = -3.22 \)  
(Round to two decimal places as needed.)

**c. What is the P-value?**

P-value = ☐  
(Round to four decimal places as needed.)

---

**Calculator Display Explanation:**

The display shows the results of a one-proportion z-test:

- **prop < 0.11**: The alternative hypothesis tested is that the proportion is less than 0.11.
- **z = -3.217067115**: The calculated z-test statistic is approximately -3.22, which indicates how far the sample proportion is from the hypothesized proportion under the null hypothesis.
- **p = 0.0006475415**: This is the P-value of the test, which indicates the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.
- **p̂ = 0.0511945392**: The observed sample proportion, calculated as 15 divided by 293.
- **n = 293**: The total number of subjects in the sample.
Transcribed Image Text:A certain drug is used to treat asthma. In a clinical trial of the drug, 15 of 293 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 11% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below. - Two-tailed test **b. What is the test statistic?** \( z = -3.22 \) (Round to two decimal places as needed.) **c. What is the P-value?** P-value = ☐ (Round to four decimal places as needed.) --- **Calculator Display Explanation:** The display shows the results of a one-proportion z-test: - **prop < 0.11**: The alternative hypothesis tested is that the proportion is less than 0.11. - **z = -3.217067115**: The calculated z-test statistic is approximately -3.22, which indicates how far the sample proportion is from the hypothesized proportion under the null hypothesis. - **p = 0.0006475415**: This is the P-value of the test, which indicates the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. - **p̂ = 0.0511945392**: The observed sample proportion, calculated as 15 divided by 293. - **n = 293**: The total number of subjects in the sample.
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