Answered: In 2010, an online security firm…

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

In 2010, an online security firm estimated that 61% of computer users don't change their passwords very often. Because this estimate may be outdated, suppose that you want to carry out a new survey to estimate the proportion of students at your school who do not change their password. You would like to determine the sample size required to estimate this proportion to within a margin of error of 0.05 with 95% confidence.

Using 0.61 as a preliminary estimate, what is the required sample size if you want to estimate this proportion with a margin of error of 0.05? (Round your answer up to the nearest whole number.)

Calculate the required sample size using the conservative value of 0.5. (Round your answer up to the nearest whole number.)

What sample size would you recommend? Justify your answer.

In 2010, an online security firm estimated that 61% of computer users don't change their passwords very often. Because this estimate may be outdated, suppose that you want to carry out a new
survey to estimate the proportion of students at your school who do not change their password. You would like to determine the sample size required to estimate this proportion to within a margin of
error of 0.05 with 95% confidence.
n USE SALT
(a) Using 0.61 as a preliminary estimate, what is the required sample size if you want to estimate this proportion with a margin of error of 0.05? (Round your answer up to the nearest whole
number.)
366
Calculate the required sample size using the conservative value of 0.5. (Round your answer up to the nearest whole number.)
385
How do the two sample sizes compare?
The sample size calculated using 0.61 is smaller than v
the sample size calculated using the conservative estimate.
(b) What sample size would you recommend? Justify your answer.
The conservative estimate
margin of error no greater than 0.05 if p > 385
vV should be used for this study because it will guarantee a margin of error of no greater than 0.05. The other sample size calculated will only guarantee a
|× or if p < 385

Expert Solution

Step 1

Given,

p = 0.61

Margin of error = E = 0.05

$α = 0.05$

The critical value is calculaed as follows:

$Z_{α / 2} = Z_{0.05 / 2} = Z_{0.025} = 1.96 . . . . . . . . . . . . . . U \sin g Z t a b l e$

To find

a) Using 0.61 as a preliminary estimate, what is the required sample size if you want to estimate this proportion with a margin of error of 0.05? (Round your answer up to the nearest whole number.)

b) Calculate the required sample size using the conservative value of 0.5. (Round your answer up to the nearest whole number.)

c) What sample size would you recommend? Justify your answer.

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