Consider the following population: {14, 16, 18, 20}. Note that the population me
ID: 3175016 • Letter: C
Question
Consider the following population: {14, 16, 18, 20}. Note that the population mean is the following. mu = (14+16+18+20)/4=17(a) 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): 14, 16 14, 18 14, 20 16, 14 16, 18 16, 20 18, 14 18, 16 18, 20 20, 14 20, 16 20, 18 Compute the sample mean for each of the 12 possible samples. Sample Sample Mean Sample Sample Mean 14, 16 18, 14 14, 18 18, 16 14, 20 18, 20 16, 14 20, 14 16, 18 20, 16 16, 20 20, 18
Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.) Maple Generated Plot Use the histogram to complete the table. (Enter the probabilities as fractions.) Column Sample Mean Probability A B C D E
(b) 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. (Enter the probabilities as fractions.)
Use the histogram to complete the table. Column Sample Mean Probability a b c d e f g
(c) In what ways are the two sampling distributions of Parts (a) and (b) similar? (Select all that apply.) They both cover the same range. They are dispersed equally. They are both symmetric about the population mean.
In what ways are they different? (Select all that apply.) One distribution covers larger range. The distributions have different mean. One distribution is more scattered than another.
o 14% ooooo AT&T; 11:40 AM webassign net Consider the following population: {14, 16, 18, 20 Note that the population mean is the following. 14+16+18+20 (a) 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) 14,16 14, 18 14, 20 16, 14 16.18 15.20 B, 14 18, 16 20 20, 14 20.16 Compute the sample mean for each of the 12 possible samples. Sample Sample Mean sample Samole Mean Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.) Sample Use the histogram to complete the table. (Enter the probabilities as fractions.) Column Sample Mean Pretabiity (b) 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. (Enter the probabilities as fractions.)
Explanation / Answer
Given, population values (14,16,18,20)
A.a) samples of size 2 are teken from the population
sample means for the 12 possible samples is given as
Values
Mean
sample 1
14
16
15
sample 2
14
18
16
sample 3
14
20
17
sample 4
16
14
15
sample 5
16
18
17
sample 6
16
20
18
sample 7
18
14
16
sample 8
18
16
17
sample 9
18
20
19
sample 10
20
14
17
sample 11
20
16
18
sample 12
20
18
19
Sampling distribution is given as
Column
Sample mean
Count
Probability
A
15
2
0.17
B
16
2
0.17
C
17
4
0.33
D
18
2
0.17
E
19
2
0.17
A.b) sampling done with replacement with sample size as 2
the 16 different set of combinations are
Values
Mean
sample 1
14
16
15
sample 2
14
18
16
sample 3
14
20
17
sample 4
16
14
15
sample 5
16
18
17
sample 6
16
20
18
sample 7
18
14
16
sample 8
18
16
17
sample 9
18
20
19
sample 10
20
14
17
sample 11
20
16
18
sample 12
20
18
19
sample 13
14
14
14
sample 14
16
16
16
sample 15
18
18
18
sample 16
20
20
20
Sampling distribution for mean is given as,
Column
Sample mean
Count
Probability
A
14
1
0.06
B
15
2
0.13
C
16
3
0.19
D
17
4
0.25
E
18
3
0.19
F
19
2
0.13
G
20
1
0.06
A.c) part a and b are same in below manner
part a and b are different in below manner
Values
Mean
sample 1
14
16
15
sample 2
14
18
16
sample 3
14
20
17
sample 4
16
14
15
sample 5
16
18
17
sample 6
16
20
18
sample 7
18
14
16
sample 8
18
16
17
sample 9
18
20
19
sample 10
20
14
17
sample 11
20
16
18
sample 12
20
18
19