STA 2023 Lecture Notes - Lecture 8: Standard Deviation, Confidence Interval, Sampling Distribution

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12 May 2019
x bar ()
statistic mean
mu (μ)
parameter mean
p hat ()
statistic proportion
parameter proportion
statistic standard deviation
sigma (σ)
parameter standard deviation
what is the standard deviation of a sample
standard error
if not given standard deviation but given range
normal approximation for quantitative variables
~N(μ, σ/√n) aka parameter mean, parameter standard deviation/n
can i use normal approximation? (quantitative)
1. is the population normally distributed?
2. is the sample size at least n=30?
as sample size increases, the sampling distribution get closer to the
normal approximation for categorical variables
~N(p, p(1-p)/n aka mean of p and standard deviation of p(1-p)/n
can i use normal approximation? (categorical)
only if 15 successes and failures
1. np ≥15
2. n(1-p) ≥15
for confidence intervals and significance tests, we...
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