Question

A study will be carried out to estimate the percentage of citizens of a city who are in favor of having fluoridated water. How large should the sample be if you want to have at least 95% confidence that the estimate is within 0.015 of the true percentage? From previous studies it is estimated that the proportion of the population that is in favor of having fluoridated water is 0.6.

Important note: Use 3 rounded decimals in the critical value.

Answer using 4 decimals.

Answer 1

Solution: The following information has been provided: a = 0.05, E = 0.015 The provided estimate population proportion p is p=0.6. The critical value for the significance level a = 0.05 is ze = 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: 2 n 2p(1-P) (E) = 0.6(1 – 0.6) ( 1.96 0.015 = = 4097.56 Therefore, the sample size needed to satisfy the condition n > 4097.56, and it must be an integer number, we conclude that the minimum required sample size is n = 4098.