Question

You are a statistician and wish to estimate, with 90% confidence, the proportion of adults who will vote during an election. Your estimate must be accurate within 2.5% of the population proportion. Find the minimum sample size needed, using a prior study that found that 73% of the respondents said they voted during the last election.

Answer 1

Solution:

Given,

E = 2.5% = 0.025

c = 90% = 0.90

p = 73% = 0.73

1- p = 1 - 0.73 = 0.27

Now,

= 1 - c = 1 - 0.90 = 0.10

/2 = 0.05

= 1.645  (using z table)

The sample size for estimating the proportion is given by

n =

= (1.645)² * 0.73 * 0.27 / (0.025²)

= 853.372044

= 854 ..(round to the next whole number)

Answer : Required Sample size is n = 854