Answer:
(a) There are 10 possible samples of size 2.
(b) The population mean is same as the mean of sample means, 4.8.
Step-by-step explanation:
The data for the number of times each technician instructed the production foreman to shut down the manufacturing process last week is:
Technician Shutdown
Taylor 5
Hurley 4
Gupta 6
Rousche 5
Huang 4
(a)
Combinations can be used to compute the number of samples of size 2 that are possible from the provided 5 technicians.
[tex]\frac{n!}{r!(n-r)!}=\frac{5!}{2!(5-2)!}=10[/tex]
Consider the table below for all the 10 possible samples.
(b)
The population mean is:
[tex]\mu=\frac{1}{n}\sum (Shutdowns)=\frac{1}{5}\times (5+4+6+5+4)=4.8[/tex]
The population mean is 4.8.
Consider the table for the sample means as follows:
The mean of the sample means is:
[tex]\mu_{\bar x}=\frac{1}{10}\sum (Mean (X_{1}, X_{2}))=\frac{4.5+5.5+5+4.5+5+4.5+4+5.5+5+4.5}{10}=4.8[/tex]
Thus, the population mean is same as the mean of sample means.
