hypothesis tests and conditions

population mean Z-test (σ known)

• random

• normal (n ≥ 30 or normal curve)

• independent (N ≥ 10n)

population mean T-test (S known)

• random

• normal (n ≥ 30 or normal curve)

• independent (N ≥ 10n)

population proportion (p)

• random

• normal (np ≥ 10, nq ≥ 10)

• independent (N ≥ 10n)

for confidence interval:

• np̂ ≥ 10, nq̂ ≥ 10

difference of population means (μ₁ - μ₂₎

• 2 random samples

• both distributions normal: n₁ ≥ 30 or graph, n₂ ≥ 30 or graph

• both samples are independent: N₁ ≥ 10n_1, N₂ ≥ 10n₂

means of two separate groups

matched pairs (is the average different between two samples?)

• random

• differences are normal (graph)

• independent N ≥ 10n

L1 - L2 = L3

observed - expected

H_o: μ_D = 0

H_a: μ_{D ≠, <, > 0}

comparing the before and after effects

difference of population proportions (p₁ - p₂₎

• 2 random samples

• differences are normal (n₁p₁ ≥ 10, n₂p₂ ≥ 10; n₁q₁ ≥ 10, n₂q₂ ≥ 10)

• independent (N₁ ≥ 10n₁, N₂ ≥ 10n₂)

if two different groups prefer something at the same rate

chi square goodness of fit

• random

• Expected Counts ≥ 5

• independent N ≥ 10n

Ho: equal frequency

Ha: follows a varied distribution from that of the problem

single variable

chi square test of independence

• random: single random sample, multi-variable

• large sample size: expected count ≥ 5

• independence: N ≥ 10n
  

Ho: is independent

Ha: is dependent

chi square test of homogeneity of proportions

• 2 random samples

• large sample size: expected count ≥ 5

• independent: N ≥ 10n

Ho: no difference in distribution

Ha: difference in distribution

multi-variable

Linear Regression T-Test

Linear: check scatterplot (no pattern in residual plot for a line)

Independent: N ≥ 10n

Normal: normal prob plot of residuals

E: Equal variance - residual plot has equal points above & below line

R: Random