4. (5 points The number of undergraduates at Hope College is about 3000, while t

Question

4. (5 points The number of undergraduates at Hope College is about 3000, while the number of undergraduates at Michigan State University is about 30,000. At both schools a simple random sample of 5% of the undergraduates is taken and the proportion that ate breakfast that day is determined for each sample. Suppose this process were repeated over and over and a distribution proportions that ate breakfast today is made for each school. It is impossible to tell which school's distribution will have more variability Since Michigan State's population is larger, its distribution will have more variability than Hope's distribution. Since Michigan State's sample size is larger, its distribution will have less variability than Hope's distribution Since 5% was sampled from both schools, the two distributions will have almost the same amount of variability. a) b) c) d)

Explanation / Answer

Sample size for Hope college (HC) = 5% of 3000 = 150

Sample size for Michigan state university (MSU) = 5% of 30000 = 1500

Thus we see that sample size for the sampling distribution of MSU is greater than that of HC.

Since the resulting plot is a sampling distribution of sample proportions, so according to Central Limit Theorem, this distribution is normal, whose standard deviation, also called as standard error, of the mean, is calculated using tjhe relation:

SE = S/n0.5

Here, S is the standard deviation (variability) of the original population, and n is the sample size.

Assuming that the original population's Standart deviation for both HC and MSU is almost similar, so we have the following answer:

Since Michigan State's sample size is larger, so its distribution will have less variability than Hope's distribution.

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