Known example average weekly food expenditures for

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Unformatted text preview: ulation in an important way • Example: sample is biased if too many retired people ECO 3411 11 Statistic and Parameter • Sample Statistic – Any number computed from sample data • A random variable. Known – Example: Average weekly food expenditures for 100 sampled residents » Random? Yes! Due to randomness of sample selection • Population Parameter – Any number computed for the entire population • A fixed number. Unknown – Example: mean weekly food expenditures for all 77,386 residents » Do we ever know this? NO! ECO 3411 12 » But we estimate it (with error) Point Estimation • In point estimation we use the data from the sample to compute a value of a sample statistic that serves as an estimate of a population parameter. • We refer to x as the point estimator of the population mean µ. s is the point estimator of the population standard deviation σ. • p is the point estimator of the population proportion p. ECO 3411 13 Sampling Error When the expected value of a point estimator is equal to the population parameter, the point estimator is said to be unbiased. The absolute value of the difference between an unbiased point estimate and the corresponding population parameter is called the sampling error. Sampling error is the result of using a subset of the population (the sample), and not the entire population. Statistical methods can be used to make probability statements about the size of the sampling error. ECO 3411 14 Sampling Error s The sampling errors are: | x − µ| for sample mean | s −σ | for sample standard deviation | p − p| for sample proportion ECO 3411 15 Example: UCF BUSINESS STUDENTS The director of admissions would like to know the following information: – the average SAT score for the applicants, and – the proportion of applicants that want to live on campus. We will now look at two alternatives for obtaining the desired information. – Conducting a census of the entire 900 applicants – Selecting a sample of 30 applicants, ECO 3411 16 Example: UCF • Taking a Census of the 900 Applicants – SAT Scores • Population Mean ...
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