che stats

mean of linear combination: the expected value is always ______. means simply ___ or _____.

linear; add; subtract

variance of linear combination: coefficients (a) are always _______. the sign of a ______ matter for variance. variances always ____.

squared; doesn’t; add

f(var) = sigma = ?

sqrt(var)

sum of n independent, identically distributed random variables with mean μ and variance σ² : E(S_n), Var(S_n), σ_sn

n*μ, n*σ², σ*sqrt(n)

sample mean (all coefficients equal 1/n): E(X bar), Var(X bar), σ_{x bar}

μ, σ²/n, σ/sqrt(n)

difference of two independent sample means: E(X₁ bar - X₂ bar), Var(X₁ bar - X₂ bar)

μ₁ - μ₂, σ₁²/n₁ + σ₂²/n₂

if each X_i is normally distributed, the linear combination of these X_i is…

also normally distributed

uncertainty accumulates due to…

squaring coefficients

if p-value ≤ alpha…

reject the null

if p-value＞alpha…

fail to reject the null

if |test stat| > critical value

reject the null

if |test stat| ≤ critical value

fail to reject the null