The Quality Control Department employs fivetechnicians during the day shift. Lis

Question

The Quality Control Department employs fivetechnicians during the day shift. Listed below is the number oftimes each technician instructed the production foreman to shutdown the manufacturing process last week.

Technician

Shutdowns

Taylor

4

Hurley

3

Gupta

5

Rousche

3

Huang

2

a. How many different samples oftwo technicians are possible from this population?

b. List all possible samples oftwo observations each and compute the mean of each sample.

c. Compare the mean of the samplemeans with the population mean.

d. Compare the shape of thepopulation distribution with the shape of the distribution of thesample means.

Technician

Shutdowns

Taylor

4

Hurley

3

Gupta

5

Rousche

3

Huang

2

Explanation / Answer

A) There are C(5, 2) ways of selecting 2 people from a group of5. C(5, 2) = 10 B) Let T be Taylor, H be Hurley, G be Gupta, R be Rousche, and U beHuang. TH = 3.5 TG = 4.5 TR = 3.5 TU = 3 HG = 4 HR = 3 HU = 2.5 GR = 4 GU = 3.5 RU = 2.5 C) Population Mean = (4 + 3 + 5 + 3 + 2) / 5 = 3.4 Sample means = (3.5 + 4.5 + 3.5 + 3 + 4 + 3 + 2.5 + 4 + 3.5 + 2.5)/ 10 = 3.4 They're the same!

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