STA 2023 Lecture Notes - Lecture 8: Standard Deviation, Confidence Interval, Sampling Distribution
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● x bar (x̄)
statistic mean
● mu (μ)
parameter mean
● p hat (p̂)
statistic proportion
● p
parameter proportion
● s
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
range/6
● normal approximation for quantitative variables
x̄~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
mean
● normal approximation for categorical variables
p̂~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...