Everything you need to know for Stats Test II Term Test 2

• 1) Two samples are random & independent
• 2) Both samples came from two independent, normal populations
• 3) σ₁² (σ₁) and σ₂²(σ₂) are known

• 1) Two samples are random & independent
• 2) Both samples came from normal populations
• 3) σ₁² (σ₁) and σ₂²(σ₂) are unknown but equal

s_p²

we combine the information given in both samples to compute estimated variance of p₁ & p₂

we do NOT combine the information contained in both samples to compute the estimated variance

Tests the Null Hypothesis that the observed frequencies follow a pattern or theoretical distribution. The test is goodness-of-fit because the hypothesis tested is how good the observed frequencies fit a given pattern

used to test whether of not the sampled multinomial data is in agreement with the hypothesized distribution. OR Testing 3 or more unknown population proportions.

A good agreement between the observed and expected frequencies results in a small value of . A perfect agreement would result in =0. Thus the Null Hypothesis is rejected if is large [upper tail test]

INDEPENDENT or not related (HoI)

DEPENDENT or related (HAD)

H₀: P₁=P₂ vs H_A:P₁≠P₂

• A test of homogeneity involves testing the
• H₀: the proportions of elements with certain characteristics in two or more different populations are the same
• vs
• H_A: the proportions are not the same