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Unformatted text preview: CHAPTER 7 INFERENCES CONCERNING MEANS SPRING 2008 STA 3032 A point estimation ( θ ˆ ) is a rule or formula that tell us how to calculate a numerical estimate based on the measurements contained in a sample. • θ is a parameter • θ ˆ is a point estimator for θ An interval estimator is a formula that tells us how to use sample data to calculate an interval that estimates a population parameter. There are two kinds of estimates: • Point Estimate: a single value • Interval Estimate: a range of values Properties of a Point Estimator: • If the mean of the sampling distribution of an estimator θ ˆ is equal to the estimated parameter θ , then the estimator is said to be unbiased. E ( θ ˆ ) = θ • If the mean of the sampling distribution of an estimator θ ˆ is different that the estimated parameter θ , then the estimator is said to be biased. E ( θ ˆ ) ≠ θ so, the bias B = E( θ ˆ )  θ Example: A point estimator θ is used to estimate the mean weight of the student laptops at UCF. The mean is determined to be 13.5 pounds. Later the true population mean for students’ laptops at UCF is determined to be 12.5 pounds. Calculate the amount of bias associated with the estimate and the parameter. 1 Interval Estimates Interval Estimates are called Confidence Intervals (CI). Large Sample (1 α) 100% Confidence Interval for the Population Mean (µ) Large sample  n ≥ 30 < < μ σ α n Z y . 2 / n Z y σ α . 2 / + n Z y σ α . 2 / ± Where: • 2 / α Z is the Z value that locates an area of α/2 to its right. • σ is the standard deviation of the population from which the sample was selected. • n is the sample size • y is the value of the sample mean. Example: Suppose a regional computer center wants to evaluate the performance of its work memory system. One measure of performance is the average time between failures of its disk drive. To estimate this value, the center recorded the time between failures for a random sample of 45 disk drive failures. The following statistics were computed: y = 1762 hours s= 215 hours Estimate the true mean time between failures with a 90% CI. 2 Example: To test a theory, 197 swarmfounding gaps were captured in Mexico, frozen at 70 C, and then subject to a series of genetic tests. The data was used to generate an inbreeding coefficient, x, for each wasp specimen, with the following results: y = 0.044 s= 0.884s= 0....
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This note was uploaded on 04/09/2008 for the course STA 3032 taught by Professor Sapkota during the Spring '08 term at University of Central Florida.
 Spring '08
 Sapkota
 Statistics

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