Answered: Consider random samples of size 50 from…

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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Question

Consider random samples of size 50 from a population with proportion 0.25. Find the standard error of the distribution of sample proportions.

Round your answer for the standard error to three decimal places.

standard error = Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.001

Expert Solution

Step 1

Sample size = 50

Proportion = 0.25

If $n p \geq 10$ and $n (1 - p) \geq 10$ then the distribution is normal

So calculate

np = 50 x 0.25 = 12.5 $\geq$ 10

n(1-p) = 50 x (1-0.25) = 37.5 $\geq$ 10

So it is a normal distribution, the formula for standard error is

$\begin{array}{rcl} σ & = & \sqrt{\frac{p \times (1 - p)}{n}} \end{array}$

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