5. You and a friend want to estimate the proportion of undergraduates at a colle

Question

5. You and a friend want to estimate the proportion of undergraduates at a college who favor eliminating classes that begin before 8 a.m. Your friend will choose a simple random sample of 250 students. You plan to choose a simple random sample of 1000 students. Think carefully about what you’d expect the sampling distribution of the sample proportion to look like for samples of size 250 versus samples of size 1000. When compared to samples of size 250, the sampling distribution based on samples of size 1000

a) will have the same mean and the same standard deviation.

b) will have a larger mean and the standard deviation will be 1/4 as large.

c) will have a larger mean and the standard deviation will be 1/2 as large.

d) will have the same mean and the standard deviation will be 1/4 as large.

e) will have the same mean and the standard deviation will be 1/2 as large.

Explanation / Answer

The answer is (e)

The sample mean does not change with sample size and remains same as that of population mean.

The standard deviation decreases as the sample size increases with a factor of n.

Thus S.D(n=1000)/S.D(n=250)

= 250/1000 = 1/2

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