Question

We wish to estimate p to within 0.02 units with 99% confidence, but are unsure on the possible value of p. What value of p yields the largest possible sample size?

• A. p= unknown
• B. p=0.5
• C. Either p=0 or p=1
• D. p=p^ from a preliminary study

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = % = 0.02

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58    ( Using z table )

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

= (2.58 / 0.02)2 * 0.5 * 0.5

Sample size = 4160

CORRECT OPTION BB. p=0.5