Question

A research firm conducts a sample survey and discovers that 90% of people are more afraid of snakes than they are of flying. If a sample questionnaire collecting these results had 790 respondents, what is the margin of error (ME), rounded to the nearest thousandth?

Answer 1

Answer:

Different values of margin of error for different significance level.

Step-by-step explanation:

We are given the following in the question:

p =  90% = 0.9

Sample size, n  790

We have to find the margin of error.

Formula:

$z_{stat}\sqrt{\dfrac{p(1-p)}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$ME = \pm 1.96\sqrt{\dfrac{0.9(1-0.9)}{790}}\\\\ME = \pm 0.021$

$z_{critical}\text{ at}~\alpha_{0.10} = 1.64$

$ME = \pm 1.64\sqrt{\dfrac{0.9(1-0.9)}{790}}\\\\ME =\pm 0.018$

$z_{critical}\text{ at}~\alpha_{0.10} = 2.58$

$ME =\pm 2.58\sqrt{\dfrac{0.9(1-0.9)}{790}}\\\\ME =\pm 0.028$