Given no preliminary estimate of p how many business phone

Given no preliminary estimate of p , how many business phone calls should you include in a random sample to be 90% sure that the point estimate p? will be within a distance of 3% from p.

Solution

Here Margin of error E = 3% =0.03

Z_C = Z_0.90 = 1.645

No preliminary estimate of p is given so,

Sample size n = (1/4) * (Z_C / E)²

= (1/4) * (1.645/0.03)²

= 751.6736

= 752 ...(Rounding to integer value)

You should include 752 business phone calls in a random sample to be 90% sure that the point estimate phat will be within a distance of 3% from p.