In: Statistics and Probability
if you're constructing a 95% confidence interval for the MEAN of some population, and you collect a sample of size 100 that has a sample mean of x-bar=30 with a population standard deviation of _=20, then how much would the margin of error of the confidence interval be? use 3 decimal places of accuracy
Given
X̅ = 30 ...sample mean
n = 100 ...sample size
σ = 20 …population standard
deviation
For 95% confidence interval, Z-value is obtained using
the Excel function NORM.S.INV
α =
0.05
α/2 = 0.025
z = NORM.S.INV(0.025)
z = 1.96 …We use the positive value of
z
Margin of Error(ME) is given by
= 3.920
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