3) Suppose you know the true mean GPA of Howard Community College and are interested in...

3) Suppose you know the true mean GPA of Howard Community College and are interested in seeing how students in your stats class compare to the college average. Compared to the sampling distribution of the means for small samples (say n = 4), how will the sampling distribution of the means be different for larger samples (say n = 25)?

a.) The sampling distribution for n=25 will have a larger mean

b.) The sampling distribution for n=25 will have a smaller mean

c.) The sampling distribution for n=25 will have a larger standard deviation

d.) The sampling distribution for n=25 will have a smaller standard deviation

e.) The sampling distributions for n=4 and n=25 will be the same

f.) There is not enough information given to compare the sampling distributions.

Solutions

Expert Solution

Here' the answer to the question. please write back in case you've doubts.

Please note that the sampling distribution' and the population distribution' mean will remain the same. For that matter, the sample size is independent of the sample mean. i.e. For a sample size of n = 25 and n =4, the samples
mean are the same.

Also, the standard deviation for larger sample sizes will decrease.

The formula that dictates this is : sample deviation = population deviation divided by sqrt(sample size).

Hence, a, b are wrong.
Hence, c is wrong
Hence, d is correct, as higher sample size = lower sample deviation
Hence, e is wrong as deviations are different for different sample sizes
Hence, f is incorrect as D is correct

D is the correct option

orchestra answered 1 year ago

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