Question

According to a Harris Poll in 2009, 72% of those who drive and own cell phones say they use them to talk while they are driving. If you wish to conduct a survey in your city to determine what percent of the drivers with cell phones use them to talk while driving, how large a sample should be if you want your estimate to be within 0.02 with 95% confidence.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.02

The provided estimate of proportion p is, p = 0.72
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.72*(1 - 0.72)*(1.96/0.02)^2
n = 1936.17

Therefore, the sample size needed to satisfy the condition n >= 1936.17 and it must be an integer number, we conclude that the minimum required sample size is n = 1937
Ans : Sample size, n = 1937 or 1936