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STAT1051_inference_lesson3

# STAT1051_inference_lesson3 - Confidence Intervals...

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Confidence Intervals Population Mean: Small Sample

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Confidence Interval for μ : Small Samples In many cases, sample sizes may be small (n <30) and the population standard deviation may be unknown (usually that is the case).
Confidence Interval Some Reasons: Collecting large samples may involve huge costs Past records or data may be unavailable to guess about the true standard deviation σ

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Assumptions Population is normally distributed 2200 σ is unknown Sample size is small, that is, n < 30. We define t does not follow standard normal distribution. It follows another distribution called a t-distribution with (n-1) degrees of freedom. n s x t / μ - =
t distribution A bell shaped distribution (similar to z ) Symmetric around 0 Bigger “spread” compared to standard normal distribution. Heavier tails than normal. Shape depends on a parameter called degrees of freedom ( df in short) As the df goes up t distribution gets closer to the z distribution

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Comparison t-curve,df=9 z-curve 0 t-curve,df=24
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