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Inferences on p class

# Baker department of statistics g university of south

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Unformatted text preview: rtment of Statistics G. University of South Carolina; Slide 7 ˆ Sampling Distribution for p Sampling ˆ The sampling distribution of p based on large n is approximately normal. Rule of Thumb: If np > 5 and n(1-p) > 5 (preferably both > 10), then the distribution of Y and hence Y/n can be approximated with a normal distribution. G. baker, Department of Statistics G. University of South Carolina; Slide 8 Sampling Distribution for ˆ p To completely define the normal distribution of ˆ p We need the mean (expected value) and variance. G. baker, Department of Statistics G. University of South Carolina; Slide 9 ˆ Sampling Distribution of p Sampling 1-α p − zα / 2 p (1 − p ) n p p + zα / 2 p (1 − p ) n p(1 − p ) n ˆ So, at most, p will be away from p, (1-α)100% of the time. We call this (1-α)100% the level of confidence. zα / 2 G. baker, Department of Statistics G. University of South Carolina; Slide 10 Repeated Sampling of Size n 95% 95% of the time our estimate will be within p (1 − p ) 1.96 n of the truth. G. baker, Department of Statistics G. University of South Carolina; Slide 11 Standard Error We don’t know the value of p, so we will We know use p use ˆ ˆ When we use p , we have an estimate of the standard deviation for the sampling ˆ distribution of p . distribution We call this estimate the standard error. ˆ ˆ p (1 − p) n G. baker, Department of Statistics G. University of South Carolina; Slide 12 Confidence Interval for p ˆ (1 − α )100%CI for p : p ± zα / 2 ˆ ˆ p(1 − p ) n Example: ˆ ˆ p (1 − p ) ˆ 95%CI for p : p ± 1.96 n G. baker, Department of Statistics G. University of South Carolina; Slide 13 Confidence Interval Based on Confidence Normal Distribution Normal Pt Est ± ( Z Value) (Standard Error) ˆ p ± zα / 2 ˆ ˆ p (1 − p ) n Standard error is our estimate of the standard deviation for the distribution of the point G. baker, Department of Statistics G. University of South Carolina; Slide 14 estimate. Confidence Interval Estimation Airplanes approaching a runway for a landing are required to stay within...
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