(d) Setup: • You obtain a dataset from a random sample. • You double-checked your dataset, and there were no typos, and no errors. • All conditions were met to develop a confidence interval. • You develop a 94% confidence interval for the population proportion p, and your confi- dence interval is 0.465 < p <0.685. • You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population proportion is p = 0.39. Why doesn't your confidence interval contain the actual population proportion? (e) Explain why you might want to potentially use the formula n > instead of n > 4h? app (1 – p) when calculating the sample size required when finding a confidence interval h2 for the population proportion. In the formula, h represents the amount of error you are willing to accept, and p represents the sample proportion.
(d) Setup: • You obtain a dataset from a random sample. • You double-checked your dataset, and there were no typos, and no errors. • All conditions were met to develop a confidence interval. • You develop a 94% confidence interval for the population proportion p, and your confi- dence interval is 0.465 < p <0.685. • You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population proportion is p = 0.39. Why doesn't your confidence interval contain the actual population proportion? (e) Explain why you might want to potentially use the formula n > instead of n > 4h? app (1 – p) when calculating the sample size required when finding a confidence interval h2 for the population proportion. In the formula, h represents the amount of error you are willing to accept, and p represents the sample proportion.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**(d) Setup:**
- You obtain a dataset from a random sample.
- You double-checked your dataset, and there were no typos, and no errors.
- All conditions were met to develop a confidence interval.
- You develop a 94% confidence interval for the population proportion \( p \), and your confidence interval is \( 0.465 < p < 0.685 \).
- You double-checked your calculations, and everything was done correctly.
**Question:** Later, you find out that the actual population proportion is \( p = 0.39 \). Why doesn’t your confidence interval contain the actual population proportion?
**(e)** Explain why you might want to potentially use the formula
\[
n \ge \frac{{z_{\alpha/2}^2 \hat{p}(1 - \hat{p})}}{{h^2}}
\]
instead of
\[
n \ge \frac{{z_{\alpha/2}^2}}{{4h^2}}
\]
when calculating the sample size required when finding a confidence interval for the population proportion. In the formula, \( h \) represents the amount of error you are willing to accept, and \( \hat{p} \) represents the sample proportion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0393b910-875a-4ed6-a578-5b5396be78bf%2F9439b6c8-2121-424f-9bf8-292856415aa8%2Fxybhftt_processed.png&w=3840&q=75)
Transcribed Image Text:**(d) Setup:**
- You obtain a dataset from a random sample.
- You double-checked your dataset, and there were no typos, and no errors.
- All conditions were met to develop a confidence interval.
- You develop a 94% confidence interval for the population proportion \( p \), and your confidence interval is \( 0.465 < p < 0.685 \).
- You double-checked your calculations, and everything was done correctly.
**Question:** Later, you find out that the actual population proportion is \( p = 0.39 \). Why doesn’t your confidence interval contain the actual population proportion?
**(e)** Explain why you might want to potentially use the formula
\[
n \ge \frac{{z_{\alpha/2}^2 \hat{p}(1 - \hat{p})}}{{h^2}}
\]
instead of
\[
n \ge \frac{{z_{\alpha/2}^2}}{{4h^2}}
\]
when calculating the sample size required when finding a confidence interval for the population proportion. In the formula, \( h \) represents the amount of error you are willing to accept, and \( \hat{p} \) represents the sample proportion.
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