COMPUTING SAMPLE SIZE. Thomas W. Jones Manufacturing Co. has asked you to check a labor standard prepared by a recently terminated analyst. Your first task is to determine the correct sample size. Your accuracy is to be within ±5% and your confidence level at 95%. The standard deviation of the sample is 1.0 and the mean 3.00.
APPROACH \blacktriangleright You apply Equation (10-4).
Required sample size = n = \left(\frac{zs}{h\bar{x}}\right)^2 (10-4)
SOLUTION \blacktriangleright h = 0.05 \bar{x} = 3.00 s = 1.0
z = 1.96 (from Table 10.2 or Appendix I)
| TABLE 10.2 | Common z -Values |
| DESIRED CONFIDENCE (%) | Z -VALUE (STANDARD DEVIATION REQUIRED FOR DESIRED LEVEL OF CONFIDENCE) |
| 90.0 | 1.65 |
| 95.0 | 1.96 |
| 95.45 | 2.00 |
| 99.0 | 2.58 |
| 99.73 | 3.00 |
n = \left(\frac{zs}{h\bar{x}}\right)^2
n = \left(\frac{1.96 \times 1.0}{0.05 \times 3}\right)^2 = 170.74 ≈ 171
Therefore, you recommend a sample size of 171.
INSIGHT \blacktriangleright Notice that as the confidence level required increases, the sample size also increases. Similarly, as the desired accuracy level increases (say, from 5% to 1%), the sample size increases.
LEARNING EXERCISE \blacktriangleright The confidence level for Jones Manufacturing Co. can be set lower, at 90%, while retaining the same ±5% accuracy levels. What sample size is needed now? [Answer: n = 121.]
RELATED PROBLEMS \blacktriangleright 10.26, 10.27, 10.28c, 10.29b, 10.30b (10.44–10.46 are available in MyOMLab)
EXCEL OM Data File Ch10Ex3.xls can be found in MyOMLab.