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A heart fills with loving kindness is a likeable person indeed.

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Estimating Proportions and Means

Sample estimatesConfidence intervalsApproximate confidence intervals for p and

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Review

Unit: a person or object to be measured Population: collection of units about which we

want information Sample: collection of units we will measure Sample size: the number of units in a sample p: population proportion : sample proportionp̂

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Fundamental Rule for Using Data for Inference

The available data can be used to make inferences about a much larger group if the data can be considered to be representative with regard to the questions of interest.

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Estimation

Sample estimate of a numerical summary of population (a parameter) is the same numerical summary of sample (a statistic)

Eg. Sample estimate of population proportion p is sample proportion

Margin of error for k%: the difference between sample estimate and the parameter is less than margin of error for k% about k% of time.

p̂

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Estimation

A k% confidence interval (C.I.) for a parameter is an interval of values computed from sample data that includes the parameter k% of time:

Sample estimate + margin of error for k%

7p

p̂

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Approximate C.I. for p

When are both at least 10: Margin of error for k% is about

where z* is the z score from the standard normal probability table corresponding to (1/2+k/2%).

n

ppz

)ˆ1(ˆ*

)ˆ1(,ˆ pnpn

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Approximate C.I. for p

An approximate k% C.I. for p is

An approximate 95% C.I. for p is

n

ppzp

)ˆ1(ˆˆ *

n

ppp

)ˆ1(ˆ2ˆ

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Approximate C.I. for

When 1. Either the population follows normal curve 2. Or the sample size n > 30 The margin of error for k% is about

where t* is the t score from the t probabilitytable corresponding to k% and (n-1) df.

n

st*

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Approximate C.I. for

An approximate k% C.I. for is

n

stx *

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