Hypothesis Testing

Description

A-Levels Further Mathematics Slide Set on Hypothesis Testing, created by Alex Burden on 30/03/2017.
Alex Burden
Slide Set by Alex Burden, updated more than 1 year ago
Alex Burden
Created by Alex Burden over 7 years ago
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Resource summary

Slide 1

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

Slide 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

Slide 3

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

Slide 4

    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

Slide 5

    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)

Slide 6

    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)

Slide 7

    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!
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