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Unformatted text preview: 8 Statistical Inference 8.1 Estimates for Population Parameters In statistical inference, the main goal is to predict population parameters depending on sample statis- tics. In other words, to predict something about the population based on data obtained from sam- ples. Point Estimate and Interval Estimate There are two types of estimates for population parameters. Point estimate: A point estimate is a single number that is out best guess for the parameter. Interval estimate: An interval estimate is an interval of numbers within which the parameter value is believed to fall. Ex 1: Let the population parameter under consideration be the mean height of Texas Tech stu- dents. Depending on sample data, we predict that the mean height of Texas Tech students is 170 cm. This is a point estimate. Depending on sample data, we predict that the mean height of Texas Tech students is 170 3 cm. i.e. between (167, 173) cm. This is an interval estimate. Point Estimate Vs Interval Estimate A point estimate does not give us any information as to how accurate our guess could be. i.e. how close the estimate is likely to be to the actual parameter value. Hence, an interval estimate is more useful as it incorporates a margin of error which helps us to measure the accuracy of the point estimate. Point Estimation The best guess for a population parameter is to use an appropriate sample statistic. For a population proportion, use the sample proportion For a population mean, use the sample mean Properties of Point Estimators 1. A good estimator has a sampling distribution that is centered at the population parameter. 2. A good estimator has a small standard error compared to other estimators. 1 Interval Estimation Confidence Interval A confidence interval is an interval containing the most believable values for a parameter. The probability that this method produces an interval that contains the parameter is called the confidence level . This is a number chosen to be close to 1, most commonly 0.95....
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- Spring '08