Amor Manufacturing Co. of Geneva, Switzerland, has just observed a job in its laboratory in anticipation of releasing the job to the factory for production. The firm wants rather good accuracy for costing and labor forecasting. Specifically, it wants to provide a 99% confidence level and a cycle

Question

Amor Manufacturing Co. of Geneva, Switzerland, has just observed a job in its laboratory in anticipation of releasing the job to the factory for production. The firm wants rather good accuracy for costing and labor forecasting. Specifically, it wants to provide a 99% confidence level and a cycle time that is within 3% of the true value. How many observations should it make? The data collected so far are as follows:

OBSERVATION	TIME
1	1.7
2	1.6
3	1.4
4	1.4
5	1.4

Accepted Answer

First, solve for the mean, [latex]\bar{x}[/latex], and the sample standard deviation, s:

[latex]s = \sqrt{\frac{\sum{(Each sample observation - \bar{x})^2}}{Number in sample - 1}}[/latex]

OBSERVATION	[latex]x_i[/latex]	[latex]\bar{x}[/latex]	[latex]x_i-\bar{x}[/latex]	[latex](x_i-\bar{x})^2[/latex]
1	1.7	1.5	.2	0.04
2	1.6	1.5	.1	0.01
3	1.4	1.5	-.1	0.01
4	1.4	1.5	-.1	0.01
5	1.4	1.5	-.1	0.01
	[latex]\bar{x}[/latex] = 1.5			0.08 = ∑[latex](x_i-\bar{x})^2[/latex]

[latex]s = \sqrt{\frac{0.08}{n - 1}} = \sqrt{\frac{0.08}{4}}[/latex] = 0.141

Then, solve for [latex]n = \left(\frac{zs}{h\bar{x}}\right)^2 = \left[\frac{(2.58)(0.141)}{(0.03)(1.5)}\right]^2[/latex] = 65.3

where [latex]\bar{x}[/latex] = 1.5
s = 0.141
z = 2.58 (from Table 10.2)

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

h = 0.03
Therefore, you round up to 66 observations.

Question 10.SP.4: Amor Manufacturing Co. of Geneva, Switzerland, has just obse...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions