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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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