A researcher wishes to estimate with 90 confidence the propo

A researcher wishes to estimate with 90% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true population.

1. Find the minimum sample size needed, using a prior study that found that 34% of the respondents said they have high speed internet access

2. No preliminary estimate is available. Find the minimum sample size needed.

a. What is the minimum sample size needed using a prior study that found that 34% of the respondents said they have high speed internet access

b. Wjat is the minimum sample size needed assuming that no preliminary estimate is available?

Solution

Given a=0.1, |Z(0.05)|=1.645(from standard normal table)

E=0.04

So n=(Z/E)^2*p*(1-p)

=(1.645/0.04)^2*0.34*(1-0.34)

=379.52

Take n=380

For no preliminary estimate is available,

n=(1.645/0.04)^2*0.5*(1-0.5)

=422.81

Take n=423