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).

Question

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 [latex]\blacktriangleright[/latex] You apply Equation (10-4).

Required sample size = n = [latex]\left(\frac{zs}{h\bar{x}}\right)^2[/latex] (10-4)

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] h = 0.05 [latex]\bar{x}[/latex] = 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 = [latex]\left(\frac{zs}{h\bar{x}} ight)^2[/latex]
n = [latex]\left(\frac{1.96 imes 1.0}{0.05 imes 3} ight)^2[/latex] = 170.74 ≈ 171
Therefore, you recommend a sample size of 171.

INSIGHT [latex]\blacktriangleright[/latex] 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 [latex]\blacktriangleright[/latex] 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 [latex]\blacktriangleright[/latex] 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.

Question 10.EX.3: COMPUTING SAMPLE SIZE. Thomas W. Jones Manufacturing Co. has...

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