Question

1. A poll is conducted in which randomly sampled SFU community members are asked, “Do you support the construction of a gondola on Burnaby Mountain?” According to the results, 82% of respondents replied “yes”. This figure is reported to be accurate to within plus or minus 6.9 percentage points, 19 times out of 20. Explain the sentence written in bold.

Answer 1

Solution :

Given that,

n = 20

x = 19

= x / n = 19 / 20 = 0.95

1 - = 1 - 0.95 = 0.05

margin of error = E = 6.9% = 0.069

At 82% confidence level the z is,

= 1 - 82%

= 1 - 0.82 = 0.18

/2 = 0.09

Z_/2 = Z _0.09 = 1.341

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

= ( 1.341 / 0.069 )² * 0.95 * 0.05

= 17.94

sample size = n = 18