Question

A political party wishes to estimate the proportion of voters that support the party in a particular state. The party will poll a random sample of n voters from the state. Which of the following is likely to result in the largest margin of error?

a. n = 500, confidence level 95%
b. n = 500, confidence level = 99%
c. n = 500, confidence level = 90%
d. n= 300, confidence level 95%
e. n = 300, confidence level = 90%

Answer 1

Option D

Explanation:

Generally the equation for Margin of Error is mathematically given by

`M.E=Z*sqrt{(p*(1-p))/(n)}`

Condition for Largest M.E

n has to be smallest and Z value has to be largest.

Where

From options

Smallest
`n=300`

Largest Z value respects to
`\alpha=95\%`

Therefore

n= 300, confidence level 95%

Option D