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CHAPTER 6 Statistical Inference & Hypothesis Testing . 6.1 - One Sample Mean μ , Variance σ 2 , Proportion π 6.2 - Two Samples Means, Variances, Proportions μ 1 vs. μ 2 σ 1 2 vs. σ 2 2 π 1 vs. π 2 6.3 - Multiple Samples Means, Variances, Proportions
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CHAPTER 6Statistical Inference & Hypothesis Testing 6.1 - One Sample Mean μ, Variance σ2, Proportion π 6.2 - Two Samples Means, Variances, Proportions μ1vs.μ2σ12vs.σ22π1vs.π2 6.3 - Multiple Samples Means, Variances, Proportions μ1, …, μkσ12, …,σk2π1, …, πk
For any randomly selected individual, define a binary random variable: POPULATION Success Failure RANDOM SAMPLE size n Discrete random variable X = # Successes in sample (0, 1, 2, 3, …, n) • Bernoulli trials: • independentoutcomes between any two trials, • with constantP(“Success”) = , P(“Failure”) = 1 – per trial
For any randomly selected individual, define a binary random variable: POPULATION Success Failure But what if the true value of is unknown? ? RANDOM SAMPLE size n Discrete random variable X = # Successes in sample (0, 1, 2, 3, …, n) In that case… can be used as a point estimate of . But in order to form a confidence interval estimate of , we need to know the……. Sampling Distribution of Then X follows a Binomial distribution,i.e., X~ Bin(n, ), with “probability mass function” f(x) = x= 0, 1, 2, …, n. Ifn 15 and n (1 – ) 15, then via the Normal Approximation to the Binomial…
s.e. DOES depend on COMPLICATION! Compare with… Sampling Distribution of Sampling Distribution of s.e. DOES NOT depend on
s.e. DOES depend on COMPLICATION! Solution: If finding a CI, replace If finding the AR or p-value, replace Sampling Distribution of Please see the notes for an example!
