A researcher wishes to estimate with 95 confidence the propo

A researcher wishes to estimate, with 95% 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 36% of the respondents said they have high-speed internet access.

B.) No preliminary estimate available. What is the minimum sample size needed assuming that no preliminary estimate is available?

Solution

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 90% confidence is 1.645 Error = 0.01 or 1% Sample size n = [(1.645)(0.4984) / 0.01]^2 = 6721.8354 = 6722 B) Repeat part A with p=0.5 standard deviation = sqrt[(0.5)(0.5)] = 0.5 Error =0.01 The z-critical value for a 90% confidence is 1.645 Sample size n = [(1.645)(0.5) / 0.01]^2 = 6765.0625 = 6765