MATLAB: An Introduction with Applications
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![**Hypothesis Testing for Proportion of Kansas Residents Setting Off Fireworks on July 4th**
In this example, we will test whether a majority of Kansas residents planned to set off fireworks on July 4th. Specifically, we will test the following hypotheses:
- Null hypothesis (H₀): p = 0.5
- Alternative hypothesis (Hₐ): p > 0.5
Here, p represents the proportion of Kansas residents who planned to set off fireworks on July 4th.
To perform this hypothesis test, follow these steps:
1. **Set Up the Hypotheses**: As stated, our hypotheses are:
- H₀: p = 0.5 (Kansas residents are equally split on the decision to set off fireworks on July 4th)
- Hₐ: p > 0.5 (A majority of Kansas residents planned to set off fireworks on July 4th)
2. **Significance Level**: Determine the significance level (α) for the hypothesis test. In this case, the significance level is given as α = 0.01.
3. **Calculate the Test Statistic**: Use the sample data to calculate the test statistic. For a proportion hypothesis test, the test statistic is given by:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]
where:
- \(\hat{p}\) is the sample proportion
- \(p_0\) is the hypothesized population proportion (0.5 in this case)
- \(n\) is the sample size
4. **Determine the P-value**: The P-value is the probability of obtaining a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. You can calculate or look up this value using statistical software or standard normal distribution tables.
5. **Conclusion**: Compare the P-value to the significance level (α):
- If P-value ≤ α, reject the null hypothesis H₀.
- If P-value > α, do not reject the null hypothesis H₀.
Summarize your findings, including the test statistic, the P-value, and whether you reject or fail to reject the null hypothesis. This will help in drawing a conclusion about the proportion of Kansas residents who planned to set off fireworks](https://content.bartleby.com/qna-images/question/e35d795b-3b3a-45a5-a595-ba94ec33b836/6d50d843-b55f-43e7-9e97-f02307694b96/gf02qs_processed.jpeg)
Transcribed Image Text:**Hypothesis Testing for Proportion of Kansas Residents Setting Off Fireworks on July 4th**
In this example, we will test whether a majority of Kansas residents planned to set off fireworks on July 4th. Specifically, we will test the following hypotheses:
- Null hypothesis (H₀): p = 0.5
- Alternative hypothesis (Hₐ): p > 0.5
Here, p represents the proportion of Kansas residents who planned to set off fireworks on July 4th.
To perform this hypothesis test, follow these steps:
1. **Set Up the Hypotheses**: As stated, our hypotheses are:
- H₀: p = 0.5 (Kansas residents are equally split on the decision to set off fireworks on July 4th)
- Hₐ: p > 0.5 (A majority of Kansas residents planned to set off fireworks on July 4th)
2. **Significance Level**: Determine the significance level (α) for the hypothesis test. In this case, the significance level is given as α = 0.01.
3. **Calculate the Test Statistic**: Use the sample data to calculate the test statistic. For a proportion hypothesis test, the test statistic is given by:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]
where:
- \(\hat{p}\) is the sample proportion
- \(p_0\) is the hypothesized population proportion (0.5 in this case)
- \(n\) is the sample size
4. **Determine the P-value**: The P-value is the probability of obtaining a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. You can calculate or look up this value using statistical software or standard normal distribution tables.
5. **Conclusion**: Compare the P-value to the significance level (α):
- If P-value ≤ α, reject the null hypothesis H₀.
- If P-value > α, do not reject the null hypothesis H₀.
Summarize your findings, including the test statistic, the P-value, and whether you reject or fail to reject the null hypothesis. This will help in drawing a conclusion about the proportion of Kansas residents who planned to set off fireworks
Transcribed Image Text:In late June 2012, Survey USA published results of a survey stating that 56% of the 600 randomly sampled Kansas residents planned to set off fireworks on July 4th.
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