QT1 - 07 - Estimation

Estimation S Q U A N T T E C H I N T E U Q I A S E V I T 1 0 S

Why Estimation ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two kinds of Estimates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Estimator ,[object Object],[object Object],[object Object],[object Object]

Criteria for a Good Estimator ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Point Estimate ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Where are the errors here ? ,[object Object],[object Object],[object Object],[object Object]

Interval Estimate ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Back to Probability ,[object Object],[object Object],[object Object],[object Object],68.3% 95.5% 99.7%

Interval Estimate of Mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confidence Interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confidence Intervals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Is a “higher” confidence interval always better ? ,[object Object],[object Object],[object Object],[object Object],[object Object]

95% confident that the mean battery life lies between 30 – 42 months ,[object Object],[object Object],[object Object],[object Object]

Calculation of Confidence Interval Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

95% Confidence Interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Upper Confidence Limit Lower Confidence Limit ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Standard deviation is not known ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],^ ^ ^

How do we get this interval ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is our goal ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What are the steps ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Confidence Intervals Revisited ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],By looking at the probability distribution function of the estimator

Sample Size in Estimation ,[object Object]

Which distribution does the estimator follow ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],68.3% 95.5% 99.7%

The Student's t distribution ,[object Object],[object Object],[object Object],[object Object]

t-distribution instead of normal =NORMSINV( D5 +0.5) =TINV( $F5 ; G$2 )

Usage of t-table ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Binomial Distribution / Proportions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

QT1 - 07 - Estimation

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QT1 - 07 - Estimation