Question

Suppose we wish to estimate the true proportion of Victoria residents who have used the new bike lanes on Pandora Avenue, with 98% confidence.  

What sample size is needed so that the width of this confidence interval will be no more than 0.02?

Answer 1

Solution

Given,

c = 98% = 0.98

width of the interval = 0.02

So, margin of error = width/2

= 0.02/2

= 0.01

Now, we have no any idea about proportion p

In this case , take p = 0.5 and 1 - p = 0.5

Now, = 1 - c = 1 - 0.98 = 0.02

/2 = 0.01

= 2.326

Now the sample size n is

n =  

= 2.326² *0.5 * 0.5/(0.01)²

= 13525.69

= 13526