Question

We wish to estimate the proportion of campers who plan to frequent a certain park this summer. We take a simple random sample of n = 30 from the among a population of N = 300 residents in a community. We observe that 25 individuals indicate they will visit the park. Estimate the proportion p in the population who plan to visit the park and provide the standard error.

Using the results above, determine the sample size required to estimate p with a bound on the error of estimation of 0.05.

The CI is 95%.

Answer 1

Solution :

Given that,

n = 30

x = 25

= x / n = 25 / 30 = 0.83

1 - = 1 - 0.83 = 0.17

margin of error = E = 0.05

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z _0.025 = 1.96

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

= ( 1.96 / 0.05 )² * 0.83 * 0.17

= 216.81

sample size = n = 217