Question

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.

A: n = 72

B: n = 73

C: n = 103

D: n = 44

Answer 1

Solution :

Given that,

= x / n =22/100=0.22

1 - = 1 - 0.22 = 0.78

margin of error = E = 0.08

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.08)2 * 0.22 * 0.78

=72.55

Sample size = 73 rounded