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or a sampling distribution of p with sample size n, taken out of a population of size N

or a sampling distribution of p with sample size n, taken out of a population of size N

MATLAB: An Introduction with Applications
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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**Sampling Distribution of \( \hat{p} \)** For a sampling distribution of \( \hat{p} \) with sample size \( n \), taken out of a population of size \( N \): 1. ⬜ The mean is \( \mu_{\hat{p}} = 0 \) and the standard deviation is \( \sigma_{\hat{p}} = 1 \) 2. ⬜ The mean is \( \mu_{\hat{p}} = \mu \) and the standard deviation is \( \sigma_{\hat{p}} = \frac{\sigma}{\sqrt{n}} \) 3. ⬜ The mean is \( \mu_{\hat{p}} = p \) and the standard deviation is \( \sigma_{\hat{p}} = \sqrt{\frac{pq}{N}} \) 4. ⬜ The mean is \( \mu_{\hat{p}} = p \) and the standard deviation is \( \sigma_{\hat{p}} = \sqrt{\frac{pq}{n}} \) Here, \( \hat{p} \) denotes the sample proportion, \( n \) is the sample size, \( N \) is the population size, \( p \) is the population proportion, and \( q = 1 - p \).
Transcribed Image Text:**Sampling Distribution of \( \hat{p} \)** For a sampling distribution of \( \hat{p} \) with sample size \( n \), taken out of a population of size \( N \): 1. ⬜ The mean is \( \mu_{\hat{p}} = 0 \) and the standard deviation is \( \sigma_{\hat{p}} = 1 \) 2. ⬜ The mean is \( \mu_{\hat{p}} = \mu \) and the standard deviation is \( \sigma_{\hat{p}} = \frac{\sigma}{\sqrt{n}} \) 3. ⬜ The mean is \( \mu_{\hat{p}} = p \) and the standard deviation is \( \sigma_{\hat{p}} = \sqrt{\frac{pq}{N}} \) 4. ⬜ The mean is \( \mu_{\hat{p}} = p \) and the standard deviation is \( \sigma_{\hat{p}} = \sqrt{\frac{pq}{n}} \) Here, \( \hat{p} \) denotes the sample proportion, \( n \) is the sample size, \( N \) is the population size, \( p \) is the population proportion, and \( q = 1 - p \).
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