Question

Imagine that we have a population that is positively (right) skewed that has a mean of 114 and a standard deviation of 12. Using a computer simulation program, Jake creates a sampling distribution of size n=5 from this population and Alex creates a sampling distribution of size n=40 from this population. How would Alex’ and Jake’s sampling distributions compare to each other?

Group of answer choices

They would have the same mean and shape, but would differ in standard error.

They would have the same shape, but would differ in mean and standard error.

They would be exactly the same since they are drawn from the same population.

They would have the same mean, but would differ in shape and standard error.

Answer 1

Solution:

Answer is

They would have the same mean, but would differ in shape and standard error.

Explanation:

Given a positively skewed population have = 114 and = 12

Let n be the sample size. Let be the sample mean.

The sampling distribution of the has

Mean =   

SD =      

So , for any sample size , mean of sampling distribution is same.

Since it is Non Normal population , the sampling distribution is approximately normal if and only if n > 30

So shape and standard error are different for the different sample sizes.

Answer is

They would have the same mean, but would differ in shape and standard error.