50. Investment Committee A company has 200 employees, consisti...

Question

50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee.

d. Explain how the company can select a representative sample of the male and female population of employees.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A tech company employs 120 programmers, 80 specialize in software, and 40 in hardware. The company wants to create a project team of 5 programmers that represents both specialities. How should the company select a representative sample for the team? Awesome. So it appears for this particular prompt, we're ultimately trying to determine how should the company select a representative sample for this specific team that they're trying to create. So with that in mind, let's read off our multiple choice answers to see what our final answer might be. So A is randomly select 3 software and 2 hardware programmers using stratified sampling. B is randomly select 5 programmers from the entire pool. C is randomly select 4 software and 1 hardware programmers. And finally, D is select 2 software and 3 hardware programmers at random. Awesome. So first off, in order to solve this problem, let us recall and define what stratified sampling is. So as we should recall a note, stratified sampling is a method where the population is divided into distinct subgroups called strata. That share a specific characteristic. Then a random sample is taken from each subgroup. So once again, a random sample is taken from each specific subgroup, and it will be proportional to its size in the population. So why would we use stratified sampling in this particular case? Because the team needs to reflect on both software and hardware specialties, and these are clearly defined groups. Therefore, as a result, it is important to ensure that each group is fairly represented. So that means that Simple random sampling might accidentally select only software or mostly software programmers, which would lead to an unbalanced team, and that's why we cannot, we cannot use simple random sampling in this particular case. That's why we have to use stratified sampling. So, with that in mind, our first major step to solve for this particular problem is we need to divide the programmers into strata. So the software programmers are 80 out of 120. Awesome. And we also need to recall a note that the hardware programmers, so I'll put an S in quotation marks for software, and for hardware programmers it's 40 out of 120, so for hardware. So once again we're dividing, or rather we're we're dividing. The programmers into strata. And now our second step is we need to calculate the proportions of each group. So for software, it's gonna be 80, so we need to take 80 divided by 120. So once again for software. Is 80 divided by 120, which is equal to 2/3, and this is for software. And for hardware, it's 40 divided by 120, which is equal to 1/3. Fantastic. So, moving right along here, that was our 2nd step, calculate the proportions of each group. Now, our 3rd step we need to multiply these proportions by the team size of 5, so we need to take 2/3 multiplied by 5, which will give us an answer of 3.333. Which we will just round to simply 3, so it's approximately equal to 3. And that is for our software. Fantastic. And for our hardware, which I'll once again is I'm just gonna simply call it H for short. We have 13 multiplied by 5, which is equal to 1.667, which we will round to approximately 2, so that means that it will be approximately equal to 2. So that will mean that our fourth and final step is we need to use stratified random sampling to select 3 software programmers and 2 hardware programmers. And this will ultimately ensure that the team represents the company's software and hardware specialties or specialists. So that means that our final answer, without a doubt has to be multiple choice letter A, which once again states randomly select 3 software and 2 hardware programmers using stratified sampling. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee.
d. Explain how the company can select a representative sample of the male and female population of employees.

Key Concepts

Sampling Methods

Proportional Representation

Sample Size

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