Answer:
B
Step-by-step explanation:
The recommended sample size n for point estimates is:
n = NX / (N + X - 1)
where N is the population size, and X is defined as:
X = Z² p (1 - p) / E²
where Z is the critical value, p is the sample proportion, and E is the margin of error.
Assume a confidence level of level of 95% and a margin of error of 5%.
α = 0.05, Z(α/2) = 1.96
E = 0.05
Of the 40 units tested, 2 had lifespans less than 26 days. So the proportion is:
p = 2/40 = 0.05
Therefore:
X = (1.96)² (0.05) (1 - 0.05) / (0.05)²
X = 73
Given N = 2000:
n = (2000) (73) / (2000 + 73 - 1)
n = 70.45
Rounding, the recommended sample size is 70.
