A researcher wishes to estimate, with 99% confidence, the proportion of adults w

Question

A researcher wishes to estimate, with 99% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 3% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 54% 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 54% of the respondents said they have high-speed Internet access? n = (Round up to the nearest whole number as needed.)

Explanation / Answer

A) prior study that found that 54% of the respondents said they have high-speed Internet access
p= 0.54
standard deviation = sqrt[p(1-p)] = sqrt[(0.54)(0.46)] =0.4984
The z-critical value for a 95% confidence is 1.96
Error = 0.03or 3%
Sample size n = [(1.96)(0.4984) / 0.03]^2
=1060.29 = 1060

B)
Repeat part A with p=0.5
standard deviation = sqrt[(0.5)(0.5)] = 0.5
Error =0.03
The z-critical value for a 95% confidence is 1.96
Sample size n = [(1.96)(0.5) / 0.03]^2
= 1067.11

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