Suppose 227 subjects are treated with a drug that is used to treat pain and 51 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea.
Question content area bottom
Part 1
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
A.
Upper H 0​: pequals0.20
Upper H 1​: pless than0.20
B.
Upper H 0​: pequals0.20
Upper H 1​: pnot equals0.20
C.
Upper H 0​: pequals0.20
Upper H 1​: pgreater than0.20
Your answer is correct.D.
Upper H 0​: pgreater than0.20
Upper H 1​: pequals0.20
Part 2
Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is 
  
enter your response here.
​(Round to two decimal places as​ needed.)

### Part 1: Identify the Null and Alternative Hypotheses
We are testing whether **more than 20%** of the subjects develop nausea, which means this is a **one-tailed test**. The claim being tested corresponds to the alternative hypothesis \(H_1\), where \(p > 0.20\). 

The correct hypotheses are:
- **Null hypothesis \(H_0\)**: \(p = 0.20\)  
- **Alternative hypothesis \(H_1\)**: \(p > 0.20\)  

The correct answer is:
**C. \(H_0: p = 0.20\), \(H_1: p > 0.20\)**  

---

### Part 2: Calculate the Test Statistic  
We are performing a **one-proportion z-test**. The formula for the **z-test statistic** is:

\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]

Where:  
- \(\hat{p} = \frac{51}{227} \approx 0.2247\) (sample proportion)  
- \(p_0 = 0.20\) (hypothesized proportion)  
- \(n = 227\) (sample size)

---

#### Step 1: Compute the Standard Error
\[
\text{SE} = \sqrt{\frac{p_0(1 - p_0)}{n}} = \sqrt{\frac{0.20 \times (1 - 0.20)}{227}} = \sqrt{\frac{0.16}{227}} = \sqrt{0.000704} \approx 0.0265
\]

---

#### Step 2: Compute the Test Statistic
\[
z = \frac{0.2247 - 0.20}{0.0265} = \frac{0.0247}{0.0265} \approx 0.93
\]

---

### Final Answer
The test statistic for this hypothesis test is:

\[
z \approx 0.93
\]

---

Let me know if you have questions or need further clarifications!  
Here are five related questions you may find helpful:

1. How do you determine the critical value for a one-tailed z-test at the 0.01 significance level?
2. How is the p-value found from a z-score in hypothesis testing?
3. What assumptions must be satisfied for a one-proportion z-test to be valid?
4. How would the test change if the sample size or proportion of nausea cases were different?
5. What is the difference between a one-tailed and two-tailed hypothesis test?

**Tip:** Always compare the calculated z-value to the critical z-value to determine whether to reject the null hypothesis.

Suppose 227 subjects are treated with a drug that is used to treat pain and 51 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea. Part 1: Identify the null and alternative hypotheses for this test. Part 2: Identify the test statistic for this hypothesis test.

Test the claim that more than 20% of drug users develop nausea using a hypothesis test at a 0.01 significance level. This problem involves calculating the z-test statistic and understanding hypothesis testing for proportions. Suitable for undergraduate statistics or advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation