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 2
Hurley 1
Gupta 3
Rousche 5
Huang 4
a. How many samples, without replacement, of size two are possible?
b. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)
The mean of the sample means is _____
The population mean is _____
Both means are:
A. not equal
B. equal.

Answer 1

Step-by-step explanation:

From the information given:

The population size N = 5

The sample size n = 2

∴

without replacement; the number of possible samples;

`^NC_n`

=
`^5C_2`

`= (5!)/(2!(5-2)!)`

`= (5!)/(2!(3)!)`

= 10

Thus, 10 different samples of 2 technicians each are possible.

DIfferent samples

S/No possible samples Mean

1 2 1 3/2 = 1.5

2 2 3 5/2 = 2.5

3 2 5 7/2 = 3.5

4 2 4 6/2 = 3

5 1 3 4/2 = 2

6 1 5 6/2 = 3

7 1 4 5/2 = 2.5

8 3 5 8/2 = 4

9 3 4 7/2 = 3.5

10 5 4 9/2 = 4.5

Total 30

Sample distribution for the sample mean
`= \frac {30} {10}`

= 3

Population mean =
`(2+1+3+5+4)/(5)`

`=(15 )/(5)`

= 3

Thus, it is obvious that both means are equal