To find the effect of a recent policy change on employee morale, a large corporation decides to conduct an opinion survey, asking N randomly selected employees whether they are satisfied with the new policy.How many employees must be sampled in order to guarantee a sampling error (95% confidence interval) within +/− 3%? (Hint: Recall class discussion of sample size to meet error margin requirements for unknown proportions.)A survey is conducted, using the value of N chosen in part a. This survey reveals that 62.5% of the sampled employees are satisfied with the new policy.What is the 95% confidence interval for p, the proportion of all company employees that are satisfied with the new policy?What is the 99% confidence interval for p? Does the 95% confidence interval suggest that a majority of employees are satisfied with the policy? Discuss in 1 or 2 sentences.

Answered: To find the effect of a recent policy…

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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To find the effect of a recent policy change on employee morale, a large corporation decides to conduct an opinion survey, asking N randomly selected employees whether they are satisfied with the new policy.

How many employees must be sampled in order to guarantee a sampling error (95% confidence interval) within +/− 3%? (Hint: Recall class discussion of sample size to meet error margin requirements for unknown proportions.)
A survey is conducted, using the value of N chosen in part a. This survey reveals that 62.5% of the sampled employees are satisfied with the new policy.
- What is the 95% confidence interval for p, the proportion of all company employees that are satisfied with the new policy?
- What is the 99% confidence interval for p?
Does the 95% confidence interval suggest that a majority of employees are satisfied with the policy? Discuss in 1 or 2 sentences.

Expert Solution

Step 1

In order to guarantee a sampling error (95% confidence interval) within +/− 3% :

The Confidence interval should be obtained as :

$\hat{p} \pm Z_{\frac{α}{2} = 0.025} \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}$

By the problem ,

$Z_{\frac{α}{2} = 0.025} \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} < 0.03 = 1.96 \times \sqrt{\frac{0.5 (1 - 0.5)}{n}} < 0.03, [∵ a t \hat{p} = 0.5 t h e e x p r e s s i o n \sqrt{\frac{0.5 (1 - 0.5)}{n}} i s m a x i m i z e d] = \sqrt{\frac{0.5 (1 - 0.5)}{n}} < 0.015306 = \frac{0.25}{n^{2}} < 0.000234 = n^{2} > 1068.376 = n > 32.686 \Rightarrow n = 33$

Therefore, 33 employees must be sampled

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