Question

Ouranos Resorts would like to send a survey to its guests asking about their satisfaction with the new website design. It would like to have a margin of error of ±6 percent on responses with 99 percent confidence. (a) Using the conservative approach, what sample size is needed to ensure this level of confidence and margin of error? (Round up your answer to the next whole number.) Sample size (b) If Ouranos Resorts wanted the margin of error to be only ±3.0 percent, what would happen to the required sample size? (Round up your answer to the next whole number.) The sample size would ..... to .... .

Answer 1

Solution,

Given that,

=  1 - = 0.5

a) margin of error = E = 0.06

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

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

= (2.576 / 0.06)² * 0.5 * 0.5

= 460.81

sample size = n = 461

b) margin of error = E = 0.03

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

= (2.576 / 0.03)² * 0.5 * 0.5

= 1843.27

sample size = n = 1844