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At a large University to graduation rate for student body was reported to be 0.65 we...

At a large University to graduation rate for student body was reported to be 0.65 we want to compare the center spread and shape of the distribution of sample proportion graduate in 4 random samples of 8 students compared to the distribution for random samples of 80 students my question is what is the center of the distribution for samples of size 8? Another question is what is the center of the distribution for samples of size 80?

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At a large University to graduation rate for student body was reported to be 0.65 we want to compare the center spread and shape of the distribution of sample proportion graduate in 4 random samples of 8 students compared to the distribution for random samples of 80 students my question is what is the center of the distribution for samples of size 8? Another question is what is the center of the distribution for samples of size 80?

Average of the distribution for samples of size 8 = 0.65. Average of the distribution for samples of size 80 = 0.65.

Standard deviation of the distribution for samples of size 8 is sqrt(0.65*(1-0.65)/8) = 0.168634

Standard deviation of the distribution for samples of size 80 is sqrt(0.65*(1-0.65)/80) = 0.053327

Average is same for both distribution but Standard deviation decreases when sample size increases from 8 to 80.

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