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ecn10-lecture13-v1

# ecn10-lecture13-v1 - Economics 10 Introduction to...

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Economics 10: Introduction to Statistical Methods Statistical Inference

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Overview of Inference Methods for drawing conclusions about a population from sample data are called statistical inference Methods Confidence Intervals - estimating a value of a population parameter Tests of significance - assess evidence for a claim about a population Inference is appropriate when data are produced by either a random sample or a randomized experiment
Confidence Intervals

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Today: Confidence Intervals The confidence interval is a range of values with an associated probability or confidence level C . The probability quantifies the chance that the interval contains the true population parameter. Using a sample to estimate a population parameter – Estimate will be somewhat different than the true population parameter by chance (sampling variability). Can we be more informative than “somewhat different”? Ask: what interval can we say contains μ X C % of the time? Ex: what interval contains μ X 95 % of the time? A confidence interval σ is known Special case: polling – conservative bounds σ is unknown – t-distribution
When is ? When SRS + Any time the data are drawn from a normally distributed population Linear functions of normally distributed random variables are also normally distributed When SRS + large n Central Limit Theorem ( 29 2 , ~ X X i N X σ μ n N X X X 2 , ~ σ μ SRS = simple random sample

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Review: standardizing the normal curve using  z N (0,1) z x N (64.5, 2.5) N ( µ , σ /√ n ) Standardized height (no units) z = x - μ σ n Here, we work with the sampling distribution, and σ /√ n is its standard deviation (spread). Remember that σ is the standard deviation of the original population.
68-95-99.7% Rule Rule of thumb for areas under a normal ≈68% of values within 1 s.d. of the mean ≈95% of values within 2 s.d. of the mean ≈99.7% of values within 3 sd of the mean Implications for the sample mean ≈68% of estimates on interval

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