Question

Mark the following statement True or False. If you believe that the statement is false, briefly explain why you think it is false. To guarantee a margin of error of 0.034 for the population proportion p, a survey needs to have at least 1,050 respondents (assuming that the results are presented with 95% confidence). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The statement is false. Without more information, it is impossible to give minimum number of respondents that guarantee a margin of error of 0.034. O B . The statement is false. To guarantee a margin of error of 0.034 for the population proportion p, a survey needs to have at least respondents. (Type a whole number.) O C. The statement is true.

Answer 1

Sample size = Z² $\alpha$ /2 * p (1 - p) / E²

= 1.96² * 0.50 * 0.50 / 0.034²

= 831 (Rounded up to nearest integer)

The statement is false. To guarantee a margin of error pf 0.034 for population proportion p, a survey needs to

have at least 831 respondents