: Completely and thoroughly explain how the Sample Size (see Module 12) either was determined or could be determined and used by any type Manufacturing Facility. (Answer only this question.)

Solution Module 12

IET3322 Module Twelve

Minimum Sample Size

Determine the correct sample size for each of the following problems. You must show

the equation you used, the values you substituted into that equation, and your final value

of "n" to three decimal places before you round the value of "n" to a whole number. In

other words, follow the examples shown on the lecture page for this assignment.

1.

After a brief time study on a delivery job, the data showed an average time to do the

delivery job of 13.5 minutes with a standard deviation of 1.40 minutes. If we use an

alpha value of 3%, and we want our final estimate to be within 0.3 minutes of the true

value, how large a sample should be taken?

Your Answer:

Alpha = 3% or 0.030

Z-table, Z = 2.170

s = 1.40 minutes

e = 0.3 minutes

This is variable data and the variable sample size equation should be used as follows:

n = [(z) (s) / (e) ]^2

n = [(2.170) (1.40) / (0.3)]^2

n = [ 10.126667 ]^2

n = 102.549 observations or 103 observations

All sample sizes are always rounded up to the next whole number.

2. A time study analyst has collected some preliminary data on a manufacturing job. The

average time to do the job is 7.3 minutes with a standard deviation of 0.45 minutes.

The analyst wants the final estimate to be within 0.30 minutes of the true time, and

the alpha value has been established at 8%. How large a sample should be studied?

Your Answer:

Alpha = 8% or 0.080

Z-table, Z = 1.751

s = 0.45 minutes

e = 0.30 minutes

This is variable data and the variable sample size equation should be used as follows:

n = [(z) (s) / (e) ]^2

n = [(1.751) (0.45) / (0.30)

]^2

n = [ 2.6265 ]^2

n = 6.899 observations or 7 observations

All sample sizes are always rounded up to the next whole number.

3. The office operations of the company currently permits a personal factor of 16%. If the

alpha value is equal to 5% and the acceptable error is 4%, how large a sample must be

taken?

Your Answer

:

p = 16% or 0.16

e = 4% or 0.04

Alpha = 5% or 0.050

Z-table, Z = 1.960

Percentages are attribute data and the attribute sample size equation should be used as

follows:

n = [ (z)^2 ] [ ( p ) ( 1 - p ) ] / [ (e)^2 ]

n = [ (1.960)^2

] [(0.16) (1 - 0.16)] / [ (0.04)^2

]

n = [ 3.8416 ] [ 0.1344 ] / [ 0.0016 ]

n = 322.694 observations or 323 observations

All sample sizes are always rounded up to the next whole number.

4. The manufacturing area has had a historical delay percentage of 7.9%. Management

wants to verify that percentage using an alpha value of 7% and they are willing to

tolerate an acceptable error of 2%. How large a sample will be necessary?

Your Answer:

p = 7.9% or 0.079

e = 2% or 0.020

Alpha = 7% or 0.07

Z-table, Z = 1.813

Percentages are attribute data and the attribute sample size equation should be used as

follows:

n = [ (z)^2] [ ( p ) ( 1 - p ) ] / [ (e)^2 ]

n = [ (1.813)^2

] [(0.079) (1 - 0.079)] / (0.02)^2

]

n = [ 3.286969 ] [ 0.072759 ] / [ 0.0004 ]

n = 597.891 observations or 598 observations

All sample sizes are always rounded up to the next whole numbe