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CHAPTER 6 Statistical Inference & Hypothesis Testing

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 6 Statistical Inference & Hypothesis Testing

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  1. 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

  2. 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

  3. 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…

  4. s.e. DOES depend on  COMPLICATION! Compare with… Sampling Distribution of Sampling Distribution of s.e. DOES NOT depend on 

  5. 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!

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