Sampling Techniques
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What is a sampling distribution?
A sampling distribution is the probability distribution of a given sample statistic based on a random sample.
What is the formula for the standard error of the mean when sampling WITHOUT replacement from a finite population?
σ_x̄ = (σ / √n) × √[(N − n) / (N − 1)], where N is population size and n is sample size
What does the Central Limit Theorem guarantee about the sampling distribution of the sample mean?
The CLT guarantees that as sample size grows, the sampling distribution of the sample mean approaches normality regardless of the population's shape.
What is the 5% rule for applying the Finite Population Multiplier (FPM)?
Apply FPM when the sampling fraction n/N ≥ 0.05 (i.e., you are sampling 5% or more of the population)
What is the formula for the standard error of the mean?
The standard error of the mean is Sigma_x-bar = Sigma / sqrt(n), where Sigma is the population standard deviation and n is the sample size.
What is the FPM value when a bank samples n = 50 accounts from a population of N = 500 accounts without replacement?
FPM = √[(500 − 50) / (500 − 1)] = √(450 / 499) = √0.9018 ≈ 0.9496
What does the first statement of the CLT say about the mean of the sampling distribution of x-bar?
The mean of the sampling distribution of x-bar equals the population mean mu, expressed as E(x-bar) = mu.
In the bank savings accounts example, if σ = ₹600 and n = 100, what is the standard error of the mean?
σ_x̄ = 600 / √100 = 600 / 10 = ₹60
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