1. Estimation selection - Bias and efficiency

Estimation is the process of approximating something about a larger population using a measurement from a smaller sample. An estimator is a sample statistic used to estimate a population value.

Estimation is very common in the social sciences and in the media. For example, during elections, people often use polls taken from smaller samples to estimate how the national, state, or local populations will vote. Estimators can be selected according to two criteria: bias and efficiency.

An estimator is said to be _____ if the ______ is not equal to the population mean.

Given two unbiased estimators of the same population value, the estimator with the _____has lower efficiency.

A sociology researcher plans to administer a questionnaire to measure anti-Semitism in his community. The participant would respond to each statement in the questionnaire with a rating on a 5-point Likert scale, with 0 equalingstrongly disagreeand 5 equalingstrongly agree. The overall score for each participant is the mean of his or her ratings for the different statements on the questionnaire. A high mean score indicates more anti-Semitism.

Assume the professor is thinking of working with one of two research firms. Firm A works with sample sizes of 2,500, and Firm B works with sample sizes of 100. Which firm should be able to provide a more efficient estimator?

Firm A

Firm B