Hypothesis Testing

Hypothesis Testing

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

Folie 2

• 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

Folie 3

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

P-Value Testing

• 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)

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!