Hypothesis Testing

Hypothesis Testing

There are 2 types of test: Significance Testing P-Value Testing

Null Hypothesis:- the assumption about the parameter  Mean Height is 1.62m           H˅0: μ=1.62   Proportion is 0.47                  H˅0: p=0.47  Mean number per ml is 6     H˅0: λ=6

Alternate Hypothesis:- if the previous test concludes that the null hypothesis should be rejected H˅1: μ>1.62 One -tailed tests H˅1: p<0.47 Two-tailed test     H˅1: λ≠6

If dealing with population and it's Normal, use a standarised Normal Distribution: X~N(μ,σ^2) Z=X-μ/σ

The smaller the value of p, the stronger the case for the rejection of H˅0.                                 p≤0.01    there is very stong evidence to reject H˅0 0.01<p>0.05    there is strong evidence to reject H˅0                   p>0.05    there is insufficient evidence to reject H˅0 For an one-tailed test;  p-value = P(X≥x) or P(X≤x)For a two-tailed test;  p-vaule = 2P(X≥x)

P-Value Testing

Testing the mean of a distribution

A Single Value with a Random Sample of n; X̅~N(μ,σ^2/n) Z=X-μ˅0/√σ^2/n 2 means with a Random Sample of n; X̅-Y̅~N(μ˅x-μ˅y,σ^2˅x/n˅x+σ^2˅y/n˅y)

Testing the mean of a Poisson Distribution

Single Value X~Po(λ) T=X˅1 + X˅2 + ... + X˅n where X˅n are independent observations. Then T~Po(nλ) If λ is large and NOT in tables then X~Po(λ,λ)This is a normal approximation question and a continuity correction MUST be used; T~Po(nλ) → T~N(nλ,nλ)

Testing a Proportion/Binomial Probability

X~Bin(n,p)X'~Bin(n,q) - if p is not in the tables If X~Bin(n,p) with np>10 and nq>10 then; X~N(np,npq) approx. As this is now a Normal approximation, a continuity correction is NEEDED!