Answer :
Answer: 400
Step-by-step explanation:
From the question, we see that population proportion (p) = 0.15
Margin of error (m) = 5%
Confidence level = 99%
Level of significance = 100- confidence level = 1%.
The population standard deviation (s) for this data set is
√p(1-p) = √ 0.15 × (1 - 0.15)
√ 0.15 × 0.85 = 0. 1275
Margin of error = critical value × population standard deviation / √n
The critical value (c) for Constructing a 99 % confidence interval for population mean is = 2.58
m = c× √p'(1-p') /√n
We want to make n subject of the formulae, we have that
m = c√p'(1-p') /√n
m×√n = c × √p'(1-p')
√n = c × √p'(1-p') / m
n = c² × {√p'(1-p')}² / m
n = 2.58² × 0.1275/ 0.05²
n = 6.6564 × 0.01625625 / 0.0025
n = 339.47 ~ 400
Answer:
339
Step-by-step explanation:
We have that the formula would come being:
n = p (1-p) * [z (α / 2) / B] ^ 2
let p, percentage averaged (0.15)
B = 5%, 0.05 (bottom margin)
α = 1 - A
A, top margin 99%
α = 1 - 0.99 = 0.01
α / 2 = 0.005
z (0.005) = 2.58 (attached normal distribution table), the value is negative in the table but is taken as positive.
Replacing we have:
n = 0.15 * (1 - 0.15) * [2.58 / 0.05] ^ 2
n = 0.1275 * (2.58 / 0.05) ^ 2
n = 339.4764
Therefore the sample size is 339.
