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statuscvo [17]
3 years ago
6

In an inductive generalization, in order to achieve an error margin of plus or minus 3 percentage points at a confidence level o

f about 95 percent, whats the smallest random sample we can get away with, regardless of the size of the target population
Mathematics
1 answer:
ANTONII [103]3 years ago
6 0
Let n =  required random sample size.

Assume that the population standard deviation is known as σ.
Let m =  sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.

Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²

This means that the sample size is about 128 times the population variance.

Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.
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