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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 μ1 vs. μ2 σ12 vs. σ π1 vs. π2 6.3 - Multiple Samples Means, Variances, Proportions μ1, …, μk σ12, …, σk π1, …, πk
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Sampling Distributions
POPULATION X = random variable, numerical (discrete or continuous) X ~ Dist(, ) = mean 2 = variance Parameter Estimation Parameters RANDOM SAMPLE size n Statistics Sampling Distributions mean variance
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Discrete random variable Sampling Distribution Sampling Distribution
POPULATION POPULATION Success Failure For any randomly selected individual, first define a binary random variable: Parameter Estimate = ? Parameter RANDOM SAMPLE size n Discrete random variable X = # Successes in sequence of n Bernoulli trials (0, …, n) Sampling Distribution Sampling Distribution
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Discrete random variable Sampling Distribution Sampling Distribution
POPULATION POPULATION Success Failure For any randomly selected individual, first define a binary random variable: Parameter Estimate = ? Parameter RANDOM SAMPLE size n Discrete random variable X = # Successes in sequence of n Bernoulli trials (0, …, n) If n 15 and n (1 – ) 15, then via the Normal Approximation to the Binomial… Sampling Distribution Sampling Distribution
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Discrete random variable Sampling Distribution Sampling Distribution
POPULATION Success Failure POPULATION For any randomly selected individual, first define a binary random variable: Parameter Estimate = ? Parameter RANDOM SAMPLE size n Discrete random variable X = # Successes in sequence of n Bernoulli trials (0, …, n) If n 15 and n (1 – ) 15, then via the Normal Approximation to the Binomial… s.e. DOES depend on s.e. does not depend on Sampling Distribution Sampling Distribution
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Sampling Distribution
Example Null Distribution Sampling Distribution
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Example Null Distribution
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Example Null Hypothesis Alternative Hypothesis Sample n = 100
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point estimate of true
Sample n = 100 X = 10 Example Null Hypothesis Alternative Hypothesis point estimate of true 95% Margin of Error 95% Confidence Interval (for ) = does not contain null value = 0.2 Reject at = .05 Statistical significance at = .05… Evidence that < 0.2, based on study. .04 .16
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point estimate of true
Example Null Hypothesis Alternative Hypothesis Sample n = 100 X = 10 Example Null Hypothesis Alternative Hypothesis point estimate of true 95% Margin of Error 95% Acceptance Region (for H0) = does not contain null value = 0.2 Reject at = .05 Statistical significance at = .05… Evidence that < 0.2, based on study. .04 .16
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point estimate of true
Example Null Hypothesis Alternative Hypothesis Sample n = 100 X = 10 Example Null Hypothesis Alternative Hypothesis point estimate of true 95% Margin of Error 95% Acceptance Region (for H0) = does not contain point estimate = 0.1 Reject at = .05 does not contain null value = 0.2 Reject at = .05 Statistical significance at = .05… Evidence that < 0.2, based on study. .12 .28
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point estimate of true
Example Null Hypothesis Alternative Hypothesis Sample n = 100 X = 10 Example Null Hypothesis Alternative Hypothesis point estimate of true p-value = Reject at = .05, etc. .12 .28
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