BS ACCOUNTING AND FINANC
ASSIGNMENT NO#1
DEPARTMENT: MANNAGEMENT
SCIENCES
COURSE: STATISTICAL INFERENCE
SUBMITTED TO: MUHAMMAD
SHOAIB
SUBMITTED BY: AMINA TAHIR
ROLL NO: L-1088
DATE: 19 OCTOBER 2020
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Sampling Distribution of Means & Population Variance in Statistical Inference, Study notes of Statistics
Solutions to statistical inference assignment problems related to calculating the number of samples, sampling distribution of means, and population mean variance for various populations and sample sizes without and with replacement.
Typology: Study notes
2019/2020
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BS ACCOUNTING AND FINANC
ASSIGNMENT NO#
DEPARTMENT: MANNAGEMENT
SCIENCES
COURSE: STATISTICAL INFERENCE
SUBMITTED TO: MUHAMMAD
SHOAIB
SUBMITTED BY: AMINA TAHIR
ROLL NO: L- 1088
DATE: 19 OCTOBER 2020
14.27) Given the population 2,4,8,8,10,10.
i. How many samples of size n=2 can be drawn without
replacement from this population?
GIVEN DATA:
N=2,4,8,8,10,
n= 2 (W.O.R)
SOLUTION:
๐ถ
๐
6!
( 6 โ 2 )! 2!
6 ร 5 ร 4 ร 3 ร 2 ร 1
( 4 ร 3 ร 2 ร 1 )( 2 ร 1 )
ii. Compute and tabulate the sampling distribution of the
mean for samples of size n=
SAMPLES:
X X
3
No. of samples =
N= 2,2,4,4,6,8,
n= 2(W.O.R)
๐
๐
7 ร 6 ร 5 ร 4 ร 3 ร 2 ร 1
( 5 ร 4 ร 3 ร 2 ร 1 )( 2 ร 1 )
STEP#
X ๐
2
3
No of samples=
2
2
2
Samples:
STEP#
X X
624
21
108
21
2
PROOF:
๐
Hence Proved
- V(x) or ฯ
๐ฅ
2
๐
2
๐
ร
๐โ๐
๐โ 1
- 86
2
ร
7 โ 2
7 โ 1
=3.93ร
5
6
Hence Proved
14.31) Draw all possible samples of size n=3 with
replacement from the population 3,6,9,12. From a sampling
distribution of the sample means. Hence state and verify
the relation between
i. Mean of the sampling distribution of the mean and the
population mean;
N=3,6,9,
n=3 (W.R)
no. of samples= 4
3
2
1
0
X ๐
2
2
2
โ [
ฮฃX
]
2
270
4
2
X X
X Tally F F/X
๐
๐
3 I 1 1/64 3/64 9 9/
4 III 3 3/64 12/64 16 48/
5 IIII I 6 6/64 30/64 25 150/
6 IIII IIII 10 10/64 60/64 36 360/
7 IIII IIII II 12 12/64 84/64 49 588/
8 IIII IIII II 12 12/64 96/64 64 768/
9 IIII IIII 10 10/64 90/64 81 810/
10 IIII I 6 6/64 60/64 100 600/
11 III 3 3/64 33/64 121 363/
12 I 1 1/64 `12/64 144 144/
๐
= ฮฃX (
F
X
V(X)=ฮฃ๐
2
๐น
๐
) โ [ฮฃ๐. (
๐น
๐
)]
2
=
3840
64
โ ( 7. 5 )
2
14.32) A population of N=5 has the following values:
a) Find the population mean and variance.
X
๐
no of samples:๐
๐ถ
๐
๐!
( ๐โ๐
) !๐!
5!
( 5 โ 3 )! 3!
5 ร 4 ร 3 ร 2 ร 1
( 2 ร 1 )( 3 ร 2 ร 1 )
x x
X Tally F F/X โX(F/X) ๐
2
2
16/3 I 1 1/10 16/30 256/9 256/
6 I 1 1/10 6/10 36 36/
19/3 I 1 1/10 19/30 361/9 361/
20/3 I 1 1/10 20/30 400/9 400/
7 II 2 2/10 14/10 49 98/
23/3 I 1 1/10 23/30 529/9 529/
2
8 I 1 1/10 8/10 64 64/
22/3 I 1 1/10 22/30 484/9 484/
26/3 I 1 1/10 26/30 676/9 676/
E(X) or๐
๐ฅ
๐
๐ฅ
= 7
V(x) or ๐
๐ฅ
2
2
๐
๐ฅ
) โ [ฮฃ๐ (
๐น
๐
)]
2
748
15
2
=
๐๐
๐๐