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handout_14 DETERMINATION OF SAMPLE SIZE

# handout_14 DETERMINATION OF SAMPLE SIZE - Apr 509...

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Apr 5’09 DETERMINATION OF SAMPLE #14 SIZE FOR ESTIMATING MEANS An important question of how large a sample to take arises early in the planning of any statistical survey or experiment. To take a larger sample than is needed to achieve the desired result is wasteful of resources and time, whereas very small samples often lead to results that are of no practical use. Let us consider a method for determining a sample size required for estimating a population mean . Objectives . The objective in interval estimation (see handout #10 ) is to obtain a narrow confidence interval estimator ± (reliability coefficient)*(standard error) (14.1) with high reliability . The width of a confidence interval is determined by the magnitude of the margin error (reliability coefficient)*(standard error) since the total width of the interval is twice this amount. For a given standard error for a sampling distribution of sample means, increasing reliability means a larger reliability coefficient [ z = z (1 – α/2) ]. But a larger reliability coefficient for a fixed standard error makes for a wider interval. On the other hand, if we fix the reliability coefficient z , the only way to reduce the width of the interval is to reduce the standard error for a sampling distribution of sample means which

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handout_14 DETERMINATION OF SAMPLE SIZE - Apr 509...

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