Unit 3: Stats Sampling Distributions & Statistical Inference

Sample Mean (Sampling Distribution)

Shape: if the original is normally distributed then the sampling distribution of the mean is normally distributed, regardless of sample size (Central Limit Theorem: if n is at least 30, we will assume that the sampling distribution of the sample mean is aprrox normal)

Center: mean of the distribution is equal to μxˉ​=μ

Spread: standard deviation of the distribution is equal to σx̄=σ/nsigma sub x bar end-sub equals sigma / the square root of n end-root

𝜎𝑥̄=𝜎 / √n

Standard error of the mean: 𝜎𝑥̄

Probability: for xˉ (normalcdf)

Percentile: invNorm

Sample Proportions (Sampling Distribution)

Shape: approx normal when np≥10 & n(1−p) ≥ 10

Center: μp^​​=p

Standard error of the mean: √p(1-p) / n

Probability: for p^ (normalcdf)

Percentile: invNorm

Null Hypothesis

Ho, assumed true until evidence indicates otherwise

Alternative Hypothesis

H1, is a claim to be tested

Hypothesis Test (Sample/Mean/Average)

H0 = μ =

H1 μ < =/ >

T-test

Hypothesis Test (Proportion/Percentage)

H0: p =

H1: p[ < =/ >

1 - Prop Z -test

Confidence Interval (Sample/Mean/Average)

T-Interval

Confidence Interval (Proportion)

2-Prop Z Int