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Samples of size n=36 are randomly selected from a population with mean = 125 and variance 12. Find the variance of the distribution of sample means.
Suggested Answer: B
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41 comments · newest first
ST
Stephen
9 months ago
I thought it would be higher, but I guess not!
JE
Jeannine
9 months ago
That gives us .333!
TA
Tamesha
9 months ago
I feel like the answer should be less than the population variance of 12, but I can't recall the exact calculation right now.
VI
Vicky
10 months ago
I practiced a similar question where we had to find the standard error, which is the square root of the variance of the sample means.
WI
Winfred
10 months ago
The variance of the sample means is variance/population size, so it's 12/36.
MI
Ming
10 months ago
I'm not entirely sure, but I remember something about the variance of the sample means being smaller than the population variance.
MA
Mattie
10 months ago
Totally agree, .333 is the right answer!
ME
Melda
10 months ago
Wait, is it really that low? Seems off.
MI
Miesha
11 months ago
I think we need to use the formula for the variance of the sample means, which is the population variance divided by the sample size.
MA
Maryrose
11 months ago
Ugh, I'm just not sure about this one. There are a lot of formulas and concepts to keep track of, and I'm worried I'm going to mix something up. I'll just take my best guess and hope for the best.
JO
Johnson
11 months ago
Hmm, I'm not sure about this one. Let me think it through step-by-step. Okay, I think I've got it now. The formula makes sense, and the numbers plug in nicely. I'm feeling pretty confident about this.
NA
Nan
11 months ago
No problem, I've got this. The population variance is 12, and the sample size is 36, so the variance of the sampling distribution is 12/36 = 0.333. The answer is A.
VI
Viola
12 months ago
Wait, what? I'm a little confused here. Do we need to use the sample size or the population size? And how do we find the variance of the sampling distribution again?
TH
Thad
12 months ago
Wait, I'm a little confused. Is the population mean also given? I feel like I'm missing something in the setup.
OR
Oretha
12 months ago
Easy peasy! The population variance is 12, and the sample size is 36, so the variance of the sample means should be 12 / 36 = 0.333.
EM
Emerson
1 year ago
Hmm, I'm a bit unsure about how to approach this. I need to remember the formula for the variance of sample means.
WI
Willard
1 year ago
This looks like a standard problem on the variance of sample means. I think I can handle this one.
GA
Gabriele
1 year ago
Wow, this question really has me scratching my head! I'm no statistician, but I'm pretty sure the answer involves some kind of magic formula. Maybe we should ask the population to take a vote on the correct answer. Or we could just roll a 36-sided die and see what comes up. Either way, I'm going with the answer that makes me laugh the most!
AN
Andra
1 year ago
Alright, time to put on my statistics hat! If the population has a mean of 125 and a variance of 12, and we're taking samples of size 36, the variance of the sample means should be 12/36 = 0.333. I'm feeling confident about A).
AR
Arlie
1 year ago
Great job on the statistics, it's always satisfying to figure out these calculations.
BR
Brett
1 year ago
So the variance of the sample means is 0.333, thanks for the explanation!
ST
Stephen
1 year ago
That makes sense, I agree with option A) .333.
KA
Kaitlyn
1 year ago
I think you're right, the variance of the distribution of sample means should be 0.333.
FL
Floyd
1 year ago
Okay, let me think this through. The population has a mean of 125 and a variance of 12, and we're taking samples of size 36. Hmm, I think the variance of the sample means should be 12/36 = 0.333. I'll go with A).
KI
Kiley
1 year ago
Yes, the variance of the distribution of sample means is indeed 0.333. Good job!
FE
Felicia
1 year ago
I agree, A) .333 seems like the correct choice based on the calculation.
RE
Ressie
1 year ago
I think the variance of the sample means should be 12/36 = 0.333. I'll go with A).
GA
Gayla
1 year ago
Aha, this is a classic statistics problem! The variance of the sample means is the population variance divided by the sample size. So, the answer is definitely A) 0.333. Easy peasy!
NA
Nathalie
1 year ago
So, the variance of the distribution of sample means is 0.333.
TA
Tanja
1 year ago
Yes, you're right! It's the population variance divided by the sample size.
MA
Marica
1 year ago
I think the answer is A) .333
LA
Lashunda
1 year ago
Hmm, let's see. If the population has a mean of 125 and a variance of 12, and we're taking samples of size 36, the variance of the sample means should be the population variance divided by the sample size, right? That would make it 12/36 = 0.333. I'm going with A).
TA
Tayna
1 year ago
Great, thanks for explaining that. I'll go with A) as well.
GR
Grover
1 year ago
Yes, that's correct. It's calculated by dividing the population variance by the sample size.
AL
Alpha
1 year ago
I think you're right, the variance of the distribution of sample means should be 0.333.
TA
Tawna
1 year ago
So, the correct answer is A) 0.333.
NI
Nidia
1 year ago
I agree, it makes sense to divide the population variance by the sample size to get the variance of the sample means.
TR
Trina
1 year ago
I think you're right, the variance of the distribution of sample means should be 0.333.
LI
Linn
2 years ago
Well, let's calculate it together to be sure.
EM
Emily
2 years ago
I disagree, I believe the answer is C) 2.
LI
Linn
2 years ago
I think the answer is D) 3.464.