Answer:
Step-by-step explanation:
Solution:-
- The sample size = n
- The Error of estimation, E = 0.04
- The confidence level, CI = 99%
a)
What size sample should be obtained when she uses previous estimate of p = 0.52?
- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):
Where,
- The critical value of the confidence level = 99% would be:
significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01
Z-critical = Z_α/2 = Z_0.005 = 2.575
- The required sample size (n) can be calculated:
- Hence, the minimum required sample size (n) should be = 612 adults.
b)
- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.
- Similarly, repeat the calculations for sample size (n) when p = 0.5
- Hence, the minimum required sample size (n) should be = 664 adults.