A certain drug is used to treat asthma. In a clinical trial of the drug,15of287treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than10%of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a0.05significance level to complete parts (a) through (e) below. e) Whats the final conclusion? **Text Transcription:**A certain drug is used to treat asthma. In a clinical trial of the drug, 15 of 287 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 10% 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 (c) below.**a. Is the test two-tailed, left-tailed, or right-tailed?**- ○ Left-tailed test- ○ Two-tailed test- ○ Right-tailed test**b. What is the test statistic?**z = □ (Round to two decimal places as needed.)**c. What is the P-value?**P-value = □ (Round to four decimal places as needed.)**Calculator Display:**- 1-PropZTest - prop < 0.1 - z = -2.6956181 - p = 0.003513909 - p̂ = 0.0522468008 - n = 287 **Explanation of Graphs/Diagrams:**There are no graphs or diagrams in the image provided. The content is textual, featuring a setup for hypothesis testing using the normal approximation to the binomial distribution, along with a calculator output for a one-proportion z-test. **Question:** What is the null hypothesis, and what do you conclude about it?**Identify the null hypothesis:**- **A.** $ H_0: p \neq 0.1 $- **B.** $ H_0: p < 0.1 $- **C.** $ H_0: p > 0.1 $- **D.** $ H_0: p = 0.1 $**Decide whether to reject the null hypothesis. Choose the correct answer below:**- **A.** Reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.- **B.** Fail to reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.- **C.** Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.- **D.** Reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.

The aim is to check whether the proportion of treated subjects who experienced headaches is less…

Answered: A certain drug is used to treat asthma.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A certain drug is used to treat asthma. In a clinical trial of the drug,

287

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

10%

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.

e) Whats the final conclusion?

**Text Transcription:**

A certain drug is used to treat asthma. In a clinical trial of the drug, 15 of 287 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 10% 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 (c) below.

**a. Is the test two-tailed, left-tailed, or right-tailed?**

- ○ Left-tailed test
- ○ Two-tailed test
- ○ Right-tailed test

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

z = □
(Round to two decimal places as needed.)

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

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

**Calculator Display:**

- 1-PropZTest
- prop < 0.1
- z = -2.6956181
- p = 0.003513909
- p̂ = 0.0522468008
- n = 287

**Explanation of Graphs/Diagrams:**

There are no graphs or diagrams in the image provided. The content is textual, featuring a setup for hypothesis testing using the normal approximation to the binomial distribution, along with a calculator output for a one-proportion z-test.

**Question:**
What is the null hypothesis, and what do you conclude about it?

**Identify the null hypothesis:**

- **A.** $ H_0: p \neq 0.1 $
- **B.** $ H_0: p < 0.1 $
- **C.** $ H_0: p > 0.1 $
- **D.** $ H_0: p = 0.1 $

**Decide whether to reject the null hypothesis. Choose the correct answer below:**

- **A.** Reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.
- **B.** Fail to reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.
- **C.** Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.
- **D.** Reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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