Answered: A. Determine the sample size required…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

A. Determine the sample size required to estimate a population proportion to within 0.04 with 97.8% confidence, assuming that you have no knowledge of the approximate value of the sample proportion.

Sample Size =

B. Repeat part the previous problem, but now with the knowledge that the population proportion is approximately 0.26.

Sample Size =

Expert Solution

Step 1

$\mathbf{Solution}$

${\color{Blue} \mathbf{A.}}$

$\mathrm{\mathbf{given}:}$

$\mathrm{Margin \;of\; error \;(E)=0.04}$

$\mathrm{\mathbf{No\; knowledge}\; of\; the\; approximate\; value \;of\; the\; sample \;proportion\;(\hat p)=\mathbf{0.50}}$

Find z-critical value:

$\mathrm{Confidence\;level\;(C)=97.8\%}$

$\mathrm{For \;97.8\%\; confidence\; level, \;z_{\frac{\alpha }{2}}=2.290 }$

$\mathbf{Download\;link\;for\;excel\;to\;find\;z_{\frac{\alpha }{2}}:}$

https://drive.google.com/file/d/1S_b_En4yZMZPhsaGfBA2eE_M0IJFOVeW/view?usp=sharing

$\mathrm{\mathbf{formula:}\;Sample\;size\;(n)=\left [ \frac{z_{\frac{\alpha }{2}}}{E} \right ]^{2}*\left [ \hat p*(1-\hat p) \right ]}$

Plug in all the values in the formula, we get

$\mathrm{Sample\;size\;(n)=\left [ \frac{2.290}{0.04} \right ]^{2}*\left [ 0.50*(1-0.50) \right ]}$

$\mathrm{Sample\;size\;(n)=\left [ 57.25 \right ]^{2}*\left [ 0.25\right ]}$

$\mathrm{Sample\;size\;(n)=819.39}$

Round the value to the nearest whole number.

$\mathrm{Sample\;size\;(n)=\mathbf{{\color{Red} 820}}}$

Step by step

Solved in 2 steps with 23 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Proportions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions