# 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...