lecture15

# lecture15 - Determining the sample size Recall that one...

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Determining the sample size I Recall that one alternative way of reducing the width of a conﬁdence interval, while maintaining the conﬁdence level, is to increase the sample size. I This is a real issue faced by an experiment designer, who would like to decide how big the sample size he or she would like. I For example, to estimate a population mean by a potential large sample, one may want a 95% conﬁdence interval with a certain narrow width to satisfy some agency requirements. In this situation a sampling scheme has to be worked out.

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Sampling error I Let us introduce the notion, sampling error , which should be distinguished from the standard error of the sampling distribution. I The sampling error is deﬁned to be the half length of a 100(1 - α )% conﬁdence interval. In formula, it is given by z α/ 2 ± σ n ² = SE , solving it gives us n = ( z α/ 2 ) 2 σ 2 (SE) 2 . If n above is not an integer, you should round it up to make the sample size suﬃcient.
the value of σ I To calculate the sample size n , we need to know σ . In practice, one may estimate it using current available sample as data collection goes. I Or conservatively, we may use the approximate relationship, σ R / 4. You may still remember the 2 σ or 3 σ rule. I If you would use R / 4 approximation, by all means you should conservatively make your sample size a little bigger than the actual numerical value.

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Example 14.3 I Suppose the manufacturer of oﬃcial NFL footballs uses a machine to inﬂate the new balls to a pressure of 13.5 pounds. When the machine is properly calibrated, the mean inﬂation pressure is 13.5 pounds, but uncontrollable
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## This note was uploaded on 06/06/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.

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lecture15 - Determining the sample size Recall that one...

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