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5. Estimators

g. identify and describe desirable properties of an estimator;

## h. distinguish between a point estimate and a confidence interval estimate of a population parameter;

What is an “estimator” and why is it important? Very often, there are a number of different estimators that can be used to estimate unknown population parameters. When faced with such a choice, it is desirable to know that the estimator chosen is the “best” under the circumstances, that is, it has more desirable properties than any of the other options available to us.

What are the three desirable properties of estimators? 1. Unbiasedness - the expected value (the mean of the sampling distribution) equals the parameter it is intended to estimate 2. Efficiency - the smallest variance compared to other unbiased estimators 3. Consistency - the probability of accurate estimates increases as the sample size increases

What is a point estimate, estimator, and estimate? - A point estimate is a single estimate of an unknown population parameter calculated as a sample mean. - The estimator is the formula used to compute the point estimate - The estimate is the specific value that is calculated using the estimator

What is a confidence interval (degree of confidence)? Confidence interval is the probability (the degree of confidence) that the interval will contain the parameter it is estimating. It is often referred to as the (1 - \alpha)% confidence interval.

What is the opposite of the confidence interval? Significance level is the opposite of confidence interval. E.g. if the degree of confidence was 95%, then the level of significance is 5%.

Assume a 95% confidence interval that the population mean is between 20-40. What does it mean? - There is a 95% probability that the population mean lies in the range of 20 to 40. - “95%” is the degree of confidence. - “5%” is the level of significance. - 20 and 40 are the lower and higher confidence limits, respectively.