A certain drug is used to treat asthma. In a clinical trial of the drug,15 of 286 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 12% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a0.05 significance level to complete parts (a) through (e) below. a. Is the test two-tailed, left-tailed, or right-tailed?b. What is the test statistic? z=c.What is the P-value? P-value equalsd.What is the null hypothesis, and what do you conclude about it?e. What is the final conclusion? **One-Proportion Z-Test Summary**- **Hypothesis Test**: 1-PropZTest- **Null Hypothesis**: Proportion (prop) < 0.12- **Test Statistic (z)**: -3.515540831- **P-Value (p)**: 0.0002194296- **Sample Proportion (\( \hat{p} \))**: 0.0524475524- **Sample Size (n)**: 286This output is from a one-proportion z-test, which is used to determine if the proportion of a single sample is significantly different from a specified population proportion. The test statistic (z) indicates how many standard deviations our sample proportion is from the hypothesized proportion, and the p-value helps in deciding whether to reject the null hypothesis. A p-value of 0.0002194296 indicates strong evidence against the null hypothesis, suggesting the sample proportion is significantly different from 0.12 at common significance levels.

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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,

15 of 286 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 12% 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.

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

b. What is the test statistic? z=

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

d.What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

**One-Proportion Z-Test Summary**

- **Hypothesis Test**: 1-PropZTest
- **Null Hypothesis**: Proportion (prop) < 0.12
- **Test Statistic (z)**: -3.515540831
- **P-Value (p)**: 0.0002194296
- **Sample Proportion (\( \hat{p} \))**: 0.0524475524
- **Sample Size (n)**: 286

This output is from a one-proportion z-test, which is used to determine if the proportion of a single sample is significantly different from a specified population proportion. The test statistic (z) indicates how many standard deviations our sample proportion is from the hypothesized proportion, and the p-value helps in deciding whether to reject the null hypothesis. A p-value of 0.0002194296 indicates strong evidence against the null hypothesis, suggesting the sample proportion is significantly different from 0.12 at common significance levels.

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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