BSB123 Lecture Notes - Lecture 12: Consistent Estimator, Interval Estimation, Confidence Interval
Estimation
- Similar to hypothesis testing in terms of goals
oHypothesis testing: determine the strength of evidence against hypothesised value
oEstimation: process of using sample data to determine the value of a population
parameter, for which there is little or no idea of the true value
- Point Estimate
oStatistic calculated from a sample of a population to estimate the unknown
population parameter
oAllows no margin for error
oDoes not use all sample information
oUnlikely any single point estimate will exactly equal the population parameter
- Interval Estimate
oAlso known as confidence intervals
oEstimates for a given parameter that allow a margin for error in estimating the
parameter
oAllows for
Sample size
Variability of data
Degree of certainty that we have of the interval containing the true
population parameter (level of confidence)
oHowever, it is still possible that the interval estimate will not contain the true
population value of the parameter of interest
Sample could be extremely unrepresentative of the population
oPlace probabilities of the distances that the estimates might be from the true
population value (calculate the chance the interval estimate will not contain the true
population value)
oRule of thumb for normal distributions
Approximately 68% of observations for the distribution lie within one
standard deviation from the mean (68% of the possible values for the
sample statistic lie within +/- 1 standard deviation of the population mean)
Approximately 95% of observations for the distribution lie within two
standard deviations from the mean (95% of the possible values for the
sample statistic lie within +/- 2 standard deviations of the population mean)
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