Consider the following population: {2, 3, 4, 5}. For this population the mean is
ID: 3340705 • Letter: C
Question
Consider the following population: {2, 3, 4, 5}. For this population the mean is
=
= 3.5
Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account).
(a) Compute the sample mean for each of the 12 possible samples.
(b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram.
(c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.)
(d) In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.)
Their means are equal.They are both symmetrical.They both cover the same range.Their means are different.One distribution covers a larger range.One distribution is not symmetrical.
2 + 3 + 4 + 5 4Explanation / Answer
Ans:
a)
b)
top right is correct.
c)First option is correct.
d)
same:
Their means are equal.They are both symmetrical.
different:
One distribution covers a larger range.
Sample Sample Mean 2, 3 2.5 2, 4 3 2, 5 3.5 3, 2 2.5 3, 4 3.5 3, 5 4 4, 2 3 4, 3 3.5 4, 5 4.5 5, 2 3.5 5, 3 4 5, 4 4.5