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 ±5 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 ±2.5 percent, what would happen to the required sample size? (Round up your answer to the next whole number.)

Answer 1

Solution-A:

Assume p=0.50

z critical for 99%=2.576

margin of error=E=5%=0.05

n=(Z/E)^2*p*(1-p)

=(2.576/0.05)^2*(0.50)*(1-0.50)

= 663.5776

=664

Required sample size=664

ANSWER:

Required sample size=664

Solution-B:

Assume p=0.50

z critical for 99%=2.576

margin of error=E=2.5%=0.025

n=(Z/E)^2*p*(1-p)

=(2.576/0.025)^2*(0.50)*(1-0.50)

= 2654.31

=2654

Required sample size=2654

ANSWER:

Required sample size=2654