Follow PANIC acronym In a recent survey of 4276 randomly selected households, it was found that 4020 of them had telephones. Using these results, we aim to construct a 99% confidence interval estimate of the true proportion of households with telephones.### Confidence Interval Estimation Steps:**P - PARAMETER**- Describe the parameter in context. This should be a complete sentence.**A - ASSUMPTIONS**- Are we allowed to construct an interval and why?**N - NAME THE INTERVAL**- State what command you will be using to compute the interval along with the values you need.**I - INTERVAL CALCULATION**- Find the interval.**C - CONCLUSION**- Write a sentence summarizing what you have found.### Explanation- **P - PARAMETER**: The parameter of interest is the true proportion of households that have telephones. - **A - ASSUMPTIONS**: We need to verify that the sample size is large enough and the sample is random to generalize the results to the population. Typically, the conditions for constructing a confidence interval for a proportion include: - The sample is random. - The sample size is less than 10% of the population, ensuring independence. - Both np and n(1-p) are greater than 10, where n is the sample size and p is the sample proportion.- **N - NAME THE INTERVAL**: For this scenario, we use a 99% confidence interval for the population proportion. The formula to compute the interval is \[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \], where $\hat{p}$ is the sample proportion, Z is the critical value from the Z-distribution corresponding to the desired confidence level, and n is the sample size.- **I - INTERVAL CALCULATION**: Calculate the interval using the formula mentioned above. Substitute the known values: - $\hat{p} = \frac{4020}{4276}$ - Z value for 99% confidence level - n = 4276- **C - CONCLUSION**: Once the interval is calculated, a concluding sentence should summarize the findings. For instance, "We are 99% confident that the true proportion of households with telephones lies within the calculated interval."By following these

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Description: Follow PANIC acronym In a recent survey of 4276 randomly selected households, it was found that 4020 of them had telephones. Using these results, we aim to construct a 99% confidence interval estimate of the true proportion of households with telepho

Sample size is n = 4276 Number of households with telephones = 4020

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99% confidence interval estimate of the true proportion of households with telephones.

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

Follow PANIC acronym

In a recent survey of 4276 randomly selected households, it was found that 4020 of them had telephones. Using these results, we aim to construct a 99% confidence interval estimate of the true proportion of households with telephones.

### Confidence Interval Estimation Steps:

**P - PARAMETER**
- Describe the parameter in context. This should be a complete sentence.

**A - ASSUMPTIONS**
- Are we allowed to construct an interval and why?

**N - NAME THE INTERVAL**
- State what command you will be using to compute the interval along with the values you need.

**I - INTERVAL CALCULATION**
- Find the interval.

**C - CONCLUSION**
- Write a sentence summarizing what you have found.

### Explanation

- **P - PARAMETER**: The parameter of interest is the true proportion of households that have telephones.

- **A - ASSUMPTIONS**: We need to verify that the sample size is large enough and the sample is random to generalize the results to the population. Typically, the conditions for constructing a confidence interval for a proportion include:
- The sample is random.
- The sample size is less than 10% of the population, ensuring independence.
- Both np and n(1-p) are greater than 10, where n is the sample size and p is the sample proportion.

- **N - NAME THE INTERVAL**: For this scenario, we use a 99% confidence interval for the population proportion. The formula to compute the interval is \[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \],
where $\hat{p}$ is the sample proportion, Z is the critical value from the Z-distribution corresponding to the desired confidence level, and n is the sample size.

- **I - INTERVAL CALCULATION**: Calculate the interval using the formula mentioned above. Substitute the known values:
- $\hat{p} = \frac{4020}{4276}$
- Z value for 99% confidence level
- n = 4276

- **C - CONCLUSION**: Once the interval is calculated, a concluding sentence should summarize the findings. For instance, "We are 99% confident that the true proportion of households with telephones lies within the calculated interval."

By following these

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