Question 23 A researcher wishes to estimate with 90 confiden

Question 23)

A researcher wishes to estimate, with 90% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 1% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 58% of the respondents said they have high-speed Internet access. b) 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 58% of the respondents said they have high-speed Internet access? n (Round up to the nearest whole number as needed.) b) What is the minimum sample size needed assuming that no preliminary estimate is available? n = [ ] (Round up to the nearest whole number as needed.)

Solution

error,E = 0.05
alpha,a = 1-0.95 = 0.05

Za/2 = Z0.025 = 1.96

a.
p = 0.48
sample size,n >= [Za/2 / E]^2 * p(1-p)

n >= [1.96 / 0.05]^2 * 0.48(1-0.48)
n >= 383.55
n = 384

b.
Since no prior estimate is given use p=0.50 to find the bound on sample size
n >= [1.96 / 0.05]^2 * 0.5(1-0.5)
n >= 384.16
n = 385