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# A.1 properties of point estimators

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### A.1 properties of point estimators

1. 1. Properties of Point Estimators
2. 2. Point Estimate vs. Interval Estimate • Statisticians use sample statistics to use estimate population parameters. (i.e. Sample means are used to estimate population means and sample proportions are used to estimate population proportions) • A population parameter can be conveyed in two ways 1. Point Estimate: a single number that is based on sample data and represents a plausible value of the characteristic p = # of successes in sample n 2. Interval estimate: use of sample data to calculate an interval of possible values of an unknown population parameter
3. 3. Confidence Intervals • Confidence intervals are used to express the precision and uncertainty associated with a particular sampling method • A confidence Interval (CI) consists of three parts 1. Confidence Level 2. Statistics 3. Margin of Error
4. 4. • Confidence Level: describes the uncertainty of the sampling method • Statistics & Margin of Error describe the precision of the method by defining an interval estimate • Interval Estimate = sample statistic + margin of error NOTE: confidence intervals are preferred to point estimates because confidence intervals indicate precision and uncertainty of estimate EX: Suppose we compute the interval estimate of the population parameter, using a 90% confidence interval. This means if we use an identical sampling method and choose different samples to compute different interval estimates, the true population parameter’s range would be defined as: sample statistics + margin of error 90% of the time.
5. 5. Confidence Level • In confidence intervals, the confidence level (CL) plays the role of the probability part. • Describes the likelihood that a particular sampling method will generate a Confidence Interval (CI) that includes the true population parameter • To interpret: If you collect all possible samples from each given population and compute the confidence intervals for each, then a 95% confidence interval means that 95% of the interval includes the true population parameter.
6. 6. Margin of Error • Margin of Error: the range of values above and below the sample statistic in a confidence interval • EX: If a survey is given to your student body and it reports that 70% of students choose English as their favorite subject, then you can state that the survey had a 10% margin of error and confidence level of 90% which results in a confidence interval of being 90% confident that English will receive between 60% and 80% of the vote.
7. 7. Bias/ Unbiased • Bias: A preference or an inclination, especially one that inhibits impartial judgment. • Unbiased: having no bias or prejudice (being fair or impartial) • Of a sample: not affected by an irrelevant factors, variables or selectivity which influence it’s distribution; random • Of an estimator: having an expected value equal to the parameter being estimated
8. 8. Review of Variability • Variability: spread in a set of data that can be described by summary measures through means of range, interquartile range, variance and standard deviation • Range: difference between largest and smallest values in a set of data • IQR= Q3 –Q1 • Variance (σ²) = Σ( xi – μ) N Standard Deviation (σ) = √(σ²)