Question

You have been given the task of organizing a poll regarding an upcoming election. The object is to estimate the proportion of the country that will vote to keep the current government in power. You have been told to collect a sample and find a 95% confidence interval for the proportion. This interval is allowed to have a margin of error of 4%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.66. a) Calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Required sample size = Someone working on your team reports that the information suggesting that the proportion of people that will vote to keep the current government is equal to 0.66 is out of date. In fact, some recent events in politics mean that there is no safe guess at what the proportion might be. b) Based on this new information, calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Required sample size =

Answer 1

Solution :

Given that,

a)

$\hat p$ = 0.66

1 - $\hat p$ = 0.34

margin of error = E = 0.04

Z$\alpha$/2 = 1.96

sample size = n = (Z$\alpha$ / 2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (1.96 / 0.04)2 * (0.66 * 0.34)

= 539

Required sample size (n) = 539

b)

$\hat p$ = 0.50

1 - $\hat p$ = 0.50

margin of error = E = 0.04

Z$\alpha$/2 = 1.96

sample size = n = (Z$\alpha$ / 2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (1.96 / 0.04)2 * (0.50 * 0.50)

= 601

Required sample size (n) = 601