Question

3. You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 97% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults. a.)266 b.) 2944 c.) 2943 d.) 2627

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.02

At 97% confidence level

= 1 - 97%

= 1 - 0.97=0.03

/2 = 0.015

Z/2 = Z0.015  = 2.17

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

= (2.17 / 0.02)2 * 0.5 * 0.5

= 2943.06

sample size = n = 2944

correct option is = b