Estimate the following by rounding each number to hundreds; then divide to get the exact answer. 1,499 4 580
ST 512: Week One Notes MaLyn Lawhorn August 16, 2017 Estimates and Estimators ▯ Estimating occurs when we need to approximate an unknown parameter ▯ ▯ to estimate, we use data that comes in the form of random variable Y , Y , Y , ▯▯▯, Y . 1 2 3 N ▯ An estimator is the algorithm, function, or equation used to approximate ▯. ▯ An estimate is the numerical output of the estimator. Example 1 Consider the following data set of the ages that a group of individuals got married: 23, 27, 29, 26, 31, 23, 24, 24, 29, 23, 27, 30, 30, 29, 25 Suppose we wanted to find the true mean ▯ of when an individual gets married. We could use the above data set to find an estim▯ of the age when an individual gets married. We do this using the estimator 1 Y = (Y 1 Y 2 Y +3▯▯▯ + Y )N N Plugging in the actual values of the data set, we get the estimate 1 ▯ = (23 + 27 + 29 + 26 + 31 + 23 + 24 + 24 + 29 + 23 + 27 + 30 + 30 + 29 + 25) = 26:6667: 15 Note that anytime we use an estimator to find an estimate, we are assuming ”sensible sampling,” meaning that we are assuming each random variable is identically distributed and mutually inde- pendent. 1 Example 2 Let ▯ be a point estimate for some unknown parameter ▯ and let ▯ = 5. Is it reasonable to believe
