Find the appropriate minimum sample size.
-To be able to say with 95% confidence level that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be greater than or equal to
What quantity?
A) 335
B) 250
C) 192
D) 805

Question

Quizplus · Accepted Answer

The formula for calculating the minimum sample size for estimating population standard deviation is:

n = [(zα/2 * σ/σ') / E]^2

where:
n = sample size
zα/2 = the critical value for the desired confidence level (in this case, 95% = 1.96)
σ = population standard deviation (unknown)
σ' = estimated standard deviation (0.1σ, or 10% of population standard deviation)
E = margin of error (also 10% of population standard deviation)

Plugging in the values given in the question, we get:

n = [(1.96 * σ/0.1σ) / 0.1σ]^2
n = (19.6)^2
n = 385.6

Rounding up, the minimum sample size required is 386, which is closest to choice letter C (192 is too low, 250 is too low, and 805 is too high).

Find the Appropriate Minimum Sample Size