Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Hypothesis Testing for Asthma Proportion**

**Objective:** Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion addressing the original claim.

**Context:** In a sample of 167 children selected randomly from one town, 37 are found to suffer from asthma. At the 0.05 significance level, we want to test the claim that the proportion of all children in the town who suffer from asthma is 11%.

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**Steps in Hypothesis Testing:**

1. **Null Hypothesis (H0):** The proportion of children with asthma in the town is 11% (p = 0.11).

2. **Alternative Hypothesis (H1):** The proportion of children with asthma in the town is not 11% (p ≠ 0.11).

3. **Test Statistic:** Use the sample data to calculate the test statistic. This will help determine whether to reject the null hypothesis.

4. **P-value:** Calculate the P-value associated with the test statistic. This will indicate the probability of observing the sample data if the null hypothesis is true.

5. **Conclusion about the Null Hypothesis:** Compare the P-value to the significance level (0.05). If the P-value is less than the significance level, reject the null hypothesis.

6. **Final Conclusion:** Based on the conclusion about the null hypothesis, determine whether there is enough evidence to support the claim that the proportion of children with asthma is not 11%.
Transcribed Image Text:**Hypothesis Testing for Asthma Proportion** **Objective:** Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion addressing the original claim. **Context:** In a sample of 167 children selected randomly from one town, 37 are found to suffer from asthma. At the 0.05 significance level, we want to test the claim that the proportion of all children in the town who suffer from asthma is 11%. --- **Steps in Hypothesis Testing:** 1. **Null Hypothesis (H0):** The proportion of children with asthma in the town is 11% (p = 0.11). 2. **Alternative Hypothesis (H1):** The proportion of children with asthma in the town is not 11% (p ≠ 0.11). 3. **Test Statistic:** Use the sample data to calculate the test statistic. This will help determine whether to reject the null hypothesis. 4. **P-value:** Calculate the P-value associated with the test statistic. This will indicate the probability of observing the sample data if the null hypothesis is true. 5. **Conclusion about the Null Hypothesis:** Compare the P-value to the significance level (0.05). If the P-value is less than the significance level, reject the null hypothesis. 6. **Final Conclusion:** Based on the conclusion about the null hypothesis, determine whether there is enough evidence to support the claim that the proportion of children with asthma is not 11%.
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