Question

The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.

Technician	Shutdowns
Taylor	4
Hurley	2
Gupta	4
Rousche	3
Huang	2

1. How many different samples of two technicians are possible from this population?

2. List all possible samples of two observations each and compute the mean of each sample. (Round your answers to 1 decimal place.)

3. Compare the mean of the sample means with the population mean. (Round your answers to 2 decimal places.)

Answer 1

a.

Number of technicians (in the population) = 5

Number of technicians in the sample =2

Number of different samples of two technicians = = 10

b.

all possible samples of two observations each and the mean of each sample.

Sample #	Technicians	Shutdowns	Mean of the sample	Mean of the sample
1	(Taylor,Hurley)	4,2	(4+2)/2=3	3
2	(Taylor,Gupta)	4,4	(4+4)/2=4	4
3	(Taylor,Rousche)	4,3	(4+3)/2=3.5	3.5
4	(Taylor,Huang)	4,2	(4+2)/2=3	3
5	(Hurley,Gupta)	2,4	(2+4)/2=3	3
6	(Hurley, Rousche)	2,3	(2+3)/2=2.5	2.5
7	(Hurley, Huang)	2,2	(2+2)/2=2	2
8	(Gupta,Rousche)	4,3	(4+3)/2=3.5	3.5
9	(Gupta,Huang)	4,2	(4+2)/2=3	3
10	(Rousche,Huang)	3,2	(3+2)/2=2.5	2.5

c.

Population:

Technician	Shutdowns
Taylor	4
Hurley	2
Gupta	4
Rousche	3
Huang	2

Population mean = Sum of shutdowns / Number of technicians = (4+2+4+3+2)/5 = 15/5=3

Population mean = 3

Mean of the sample means

= (Sum of sample means)/Number of samples

=(3+4+3.5+3+3+2.5+2+3.5+3+2.5)/10 = 30/10 =3

Mean of the sample means = 3

Population mean = Mean of sample means