**Constructing a 99% Confidence Interval for a Population Proportion**To construct the 99% confidence interval estimate for the population proportion $ p $, we start with the given data:- Sample size ($ n $) = 300- Number of successes ($ x $) = 221Next, we follow these steps:1. Calculate the sample proportion ($ \hat{p} $). \[ \hat{p} = \frac{x}{n} = \frac{221}{300} \]2. Determine the standard error (SE) of the sample proportion. \[ SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]3. Identify the z-score corresponding to the 99% confidence level. For a 99% confidence interval, this z-score is typically 2.576.4. Calculate the margin of error (ME). \[ ME = z \times SE \]5. Finally, construct the confidence interval. \[ \hat{p} - ME < p < \hat{p} + ME \]The blank areas in the image indicate where the calculated lower and upper bounds of the confidence interval will be input. These calculations provide the range within which the true population proportion $ p $ lies with 99% confidence.

Answered: Construct the 99% confidence interval…

Construct the 99% confidence interval estimate of the population proportion p if the sample size is n = 300 and the number of successes in the sample is = 221. < p<

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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**Constructing a 99% Confidence Interval for a Population Proportion**

To construct the 99% confidence interval estimate for the population proportion $ p $, we start with the given data:

- Sample size ($ n $) = 300
- Number of successes ($ x $) = 221

Next, we follow these steps:

1. Calculate the sample proportion ($ \hat{p} $).
\[
\hat{p} = \frac{x}{n} = \frac{221}{300}
\]

2. Determine the standard error (SE) of the sample proportion.
\[
SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]

3. Identify the z-score corresponding to the 99% confidence level. For a 99% confidence interval, this z-score is typically 2.576.

4. Calculate the margin of error (ME).
\[
ME = z \times SE
\]

5. Finally, construct the confidence interval.
\[
\hat{p} - ME < p < \hat{p} + ME
\]

The blank areas in the image indicate where the calculated lower and upper bounds of the confidence interval will be input. These calculations provide the range within which the true population proportion $ p $ lies with 99% confidence.

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