066. Sample Size for the population mean

Recall that the normal deviate Z can be expressed as

Z = =

This can be rewritten algebraically as

N = (6.7)

Where the difference between the sample mean and the population mean is the error. In the Example 6.6 For the compact disk players with a tolerable error of 2 cm, Formula (6.7) would be written as

The value of Z depends on the level of confidence required. This leaves only to be determined in order to calculate the proper sample size. In the likely event is unknown, it can be estimated with a Pilot sample of any reasonable size (n > 30). The variance calculated from this preliminary sample can then be used in Formula (6.7).

Assume, for example, that the manufacturer of the disk players wishes to construct a 95 percent interval for the mean size of the part. A pilot sample has revealed a standard deviation of 6 cm in the part. How large should the sample be? A 95 percent interval calls for a Z-value of 1.96. Thus,

N =

The manufacturer should select a sample of 35 parts. From this sample, a 95 percent interval could be constructed for the mean size. This interval would have an error not greater than 2 cm.

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