**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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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der Describe the shape of the distribution. OA. The distribution is uniform. O B. The distribution is skewed to the right. OC. The distribution is skewed to the left. OD. The distribution is bell shaped.
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Describe the sampling distribution of p. Assume the size of the population is 20,000. n 800, p 0.356 Describe the shape of the sampling distribution of p. Choose the correct answer below. A. The shape of the sampling distribution of p is not normal because n s 0.05N and np(1 - p)< 10 В. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p) 10 A С. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1 -p)2 10 D. The shape of the sampling distribution of p is not normal because ns 0.05N and np(1 -p)z 10. Determine the mean of the sampling distribution of p. (Round to three decimal places as needed.) HA р Determine the standard deviation of the sampling distribution of p. (Round to three decimal places as needed.) р
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Describe the sampling distribution of p. Assume the size of the population is 30,000. n = 900, p = 0.625 Describe the shape of the sampling distribution of p. Choose the correct answer below. A. The shape of the sampling distribution of p is not normal because n ≤0.05N and np(1-p) < 10. B. The shape of the sampling distribution of p is approximately normal because n≤0.05N and np(1-p) ≥ 10. C. The shape of the sampling distribution of p is not normal because n ≤0.05N and np(1 - p) ≥ 10. р A D. The shape of the sampling distribution of p is approximately normal because n ≤0.05N and np(1-p) < 10. Determine the mean of the sampling distribution of p. (Round to three decimal places as needed.) H₁ = Determine the standard deviation of the sampling distribution of p. (Round to three decimal places as needed.) 0₁ = р

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