Name: Lou T. Recamara
Section: Faith
Solve the followingProblem:
A. Under Observation: 4, 6, 8, 10, 12, 2,
Combined the observation two at a time with replacement.
1. Construct the table of the samples and sample means.
2. Construct the Distribution table of sample mean.
3. Graph the values from number 2, using histogram.
B. Assume the population has a standard deviation 𝜎 = 12. Compute the
standard error of the sampling distribution of the sample mean 𝜎𝑥̅ if
random samples with the following sizes are taken:
1. 10
3. 30
2. 20
4. 50
5. 100
Answer: Show your Solution
A.
1. table of the samples and sample means.
4,6,8,10,12,2 = 36
Sample
4,4
4,6
4,8
4,10
4,12
4,2
6,4
6,6
6,8
6,10
6,12
6,2
8,4
8,6
8,8
8,10
8,12
8,2
Sample mean
4
5
6
7
8
3
5
6
7
8
9
4
6
7
8
9
10
5
Sample
10,4
10,6
10,8
10,10
10,12
10,2
12,4
12,6
12,8
12,10
12,12
12,2
2,4
2,6
2,8
2,10
2,12
2,2
Sample mean
7
8
9
10
11
6
8
9
10
11
12
7
3
4
5
6
7
2
2 .Sampling Distribution
x̄
P(x)
2
1
36
3
2
36
4
3
36
5
4
36
6
5
36
7
6
36
8
5
36
9
4
36
10
3
36
11
2
36
12
1
36
3.Histogram
0,18
0,16
0,14
P(x)
0,12
0,1
0,08
0,06
0,04
0,02
0
2
3
4
5
6
7
x̄
B.
Ơ=12
1.) 10
Stdrr= ơ
√n
= 12
√10
=3.79
8
9
10
11
12
2.) 20
Stdrr= ơ
√n
= 12
√20
= 2.68
3.) 30
Stdrr= ơ
√n
= 12
√30
= 2.19
4.) 50
Stdrr= ơ
√n
= 12
√50
=1. 69
5.) 100
Stdrr= ơ
√n
= 12
√100
=1. 2