Question

1 point) A polling organization has been hired to conduct a survey to determine the proportion of people who are likely to support an upcoming ballot initiative. To help determine the size of the sample required for the main poll, a preliminary poll of 20 people is taken that yields the results below. (Yes indicates that the person will support the initiative, No indicates that they won't.) NoYesNoYesNoNoNoYesNoYesYesYesNoNoNoNoNoNoYesNo No No No No No Yes No Yes No No No No Yes No Yes Yes Yes Yes No No Based on the results of the peliminary poll, how large a sample is required for the main poll, assuming that the main poll should have a margin of error of 2.7% and a confidence level of 95.5%. Sample Size =

Answer 1

Solution :

Given that,

= 14 / 20 = 0.7

1 - = 1 - 0.7 = 0.3

margin of error = E = 2.7% = 0.027

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.027)² * 0.7 * 0.3

= 1106.63 = 1107

sample size = 1107