There are 1000 random samples of size n=2. There is a mean of 100 and a standard

Question

There are 1000 random samples of size n=2. There is a mean of 100 and a standard deviation of 16.

a. Suppose that instead of looking at 1000 sample means with a sample size of n=2, we had sample sizes of n=64. The sample mean and sample standard deviation among the 1000 samples would be close to what values?

b. Suppose that instead of looking at 1000 sample means with a sample size of n=2, we had sample sizes of n=400. The sample mean and sample standard deviation among the 1000 samples would be close to what values?

Explanation / Answer

Here we will use central limit theorem for sampling distribution which says for sufficient large sample i.e. >30 mean and sd for sampling mean will be mu and sd/sqrt(n)

a. For n=64,mean=100 and sd=16/8=2

b. For n=400, mean=100 and sd=16/20=0.8

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