Simple Random Sample vs Random Sample

[kuthaman]

Problem:
"A computer company employs 100 software engineers and 100 hardware engineers. The personnel manager randomly selects 20 of the software engineers and 20 of the hardware engineers and questions them about career opportunities within the company. Does this sampling plan result in a random sample? Simple random sample? Explain?"

What I have done so far: - For a moment I thought this was both a simple random sample and a random sample, but I found out my choice was wrong. Then I guessed it was a Simple Random Sample, but not a random sample. I have included the definitions I was presented with.

A simple random sample of n subjects is selected in such a way that every possi-
ble sample of the same size n has the same chance of being chosen.

In a random sample members from the population are selected in such a
way that each individual member in the population has an equal chance of
being selected.

My Questions:

1)How do you diffreniate between these between simple random samples and random samples? (These definitions in my opinion do not clearly present the difference)

2) What is the approach to solve the problem above?

THank you in advance!!

[hlsmith]

Not sure what they are looking for in particular. Did these definitions come from the web or your coursework. I would check the web, but perhaps they are looking for a distinction between sampling those available and sampling all people fitting the definition in the entire population.

[kuthaman]

These definitions are out of my book Elementary Statistics by Triola. I have looked through the web, but I have been unable to find a clear distinction between these two concepts.

[Dason]

Let's simplify it a little bit.

Lets say you have two people in group A and two people in group B. We could label these people A1, A2, B1, B2. If we wanted to take a sample of 2 people if we were to do a simple random sample then the possibilities for our sample would be:

{{A1, A2}, {A1, B1}, {A1, B2}, {A2, B1}, {A2, B2}, {B1, B2}}.

In a simple random sample each of these possibilities has the same probability. Also note that each person has a probability of 1/2 of being selected.

However notice that it's possible to get two people from the same group. So if we used a sampling scheme where we random choose one person from each of the groups our possible samples are:

{{A1, B1}, {A2, B1}, {A1, B2}, {A2, B2}}

So in this case there are certain samples that aren't available ({A1, A2} and {B1, B2}), however, each person still has a probability of 1/2 of being selected in the sample.

[kuthaman]

I understand your logic when explaining the difference between the two terms, but I am having trouble applying the logic to the problem I have included.

[Dason]

Can your sample of 40 people ever consists of just 40 hardware engineers? If not then it isn't a simple random sample.

[kuthaman]

Problem:
"A computer company employs 100 software engineers and 100 hardware engineers. The personnel manager randomly selects 20 of the software engineers and 20 of the hardware engineers and questions them about career opportunities within the company. Does this sampling plan result in a random sample? Simple random sample? Explain?"

Solution:

Based on your post, I understand now that this is not a Simple Random Sample because every group of 40 cannot be selected(ex. 40 Software Engineers).

Please Confirm this for me: This is a Random Sample because all members of the total 200(100 Hardware Engineers and 100 Software Software Engineers) have a 1/100 chance of being selected.