Suppose you wish to conduct a survey to determine the propor

Suppose you wish to conduct a survey to determine the proportion of Bellingham residents who commute by bicycle at least once a week. You decide you would like have 90% confidence that the sample proportion is in error by not more than three percentage points. Determine the sample size needed under the following conditions. A previous study found that 32% of Bellingham residents commute by bicycle at least once a week. There are no prior estimates of the percent of Bellingham residents who commute by bicycle at least once a week.

Solution

a)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Samle Proportion = 0.32
ME = 0.03
n = ( 1.645 / 0.03 )^2 * 0.32*0.68
= 654.257 ~ 655

b)
Z a/2 at 0.1 is = 1.645
There is no prior estimation we consider the sample Proportion = 0.5
ME = 0.03
n = ( 1.645 / 0.03 )^2 * 0.5*0.5
= 751.674 ~ 752