**Title: Understanding the Sampling Distribution of the Sample Proportion****Introduction**In this exercise, we'll explore the sampling distribution of the sample proportion (\(\hat{p}\)). We are given the following parameters:- Population size (\(N\)): 30,000- Sample size (\(n\)): 1,100- Population proportion (\(p\)): 0.708**Objective**Understand the shape of the sampling distribution of \(\hat{p}\) and calculate its mean and standard deviation.**Question 1: Shape of the Sampling Distribution**Choose the correct statement regarding the shape of the sampling distribution of \(\hat{p}\):- **A.** The shape of the sampling distribution of \(\hat{p}\) is not normal because \(n \leq 0.05N\) and \(np(1-p) < 10\).- **B.** The shape of the sampling distribution of \(\hat{p}\) is approximately normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\).- **C.** The shape of the sampling distribution of \(\hat{p}\) is not normal because \(n \leq 0.05N\) and \(np(1-p) \geq 10\).- **D.** The shape of the sampling distribution of \(\hat{p}\) is approximately normal because \(n \leq 0.05N\) and \(np(1-p) < 10\).**Question 2: Determine the Mean**Calculate the mean of the sampling distribution of \(\hat{p}\):\[\mu_{\hat{p}} = \_ \_ \_ \]*(Round to three decimal places as needed.)***Question 3: Determine the Standard Deviation**Calculate the standard deviation of the sampling distribution of \(\hat{p}\):\[\sigma_{\hat{p}} = \_ \_ \_ \]*(Round to three decimal places as needed.)***Conclusion**To solve these problems, use the criteria for the normal approximation of the binomial distribution and apply the formulas for the mean and standard deviation of the sampling distribution.

It is given that N = 30000 n = 1100 p = 0.708

Answered: Describe the shape of the sampling…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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