SAMPLING DISTRIBUTIONThe following are the monthly income of 5 workers working in a different company:15 000, 18 000, 21 000, 24 000, and 28 000 (in pesos). A sample with size 2 is chosen to determine the average monthly income of the workers. Show your complete solution.Find the mean of the sample means.Compute the standard error of the sample means. Solution 1.Here, the population size is: N = 5 and the sample size is: n = 2.Since, nothing has been mentioned we will consider simple random sampling with replacement (SRSWR).In SRSWR, the number of possible sampling isN"-52=25Answer: The total number of possible outcomes is 25.Solution 2.Here we construct the the table of all possible samples and the corresponding sample means.Table of Sample MeansSample values Sample mean15000, 150001500015000, 180001650015000, 210001800015000, 240001950015000, 280002150018000, 150001650018000, 180001800018000, 210001950018000, 240002100018000, 280002300021000, 150001800021000, 180001950021000, 210002100021000, 240002250021000, 280002450024000, 150001950024000, 180002100024000, 210002250024000, 240002400024000, 280002600028000, 150002150028000, 180002300028000, 210002450028000, 240002600028000, 2800028000(Answer) Solution 3.There are 25 different possible samples, so the probability of each of the sample means isBased on this we construct the following sampling distribution of the sample means.Sampling Distribution of the Sample MeansProbaSample meanbility150001/25165002/25180003/25195004/25210003/25215002/25225002/25230002/25240001/25245002/25260002/25280001/25Total(Answer)

Given: Population size N = 5 Sample size n = 2 Formula Used: Sample mean X = ∑i=1nXin Sample…

Answered: SAMPLING DISTRIBUTION The following…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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SAMPLING DISTRIBUTION

The following are the monthly income of 5 workers working in a different company:

15 000, 18 000, 21 000, 24 000, and 28 000 (in pesos). A sample with size 2 is chosen to determine the average monthly income of the workers. Show your complete solution.

Find the mean of the sample means.
Compute the standard error of the sample means.

Solution 1.
Here, the population size is: N = 5 and the sample size is: n = 2.
Since, nothing has been mentioned we will consider simple random sampling with replacement (SRSWR).
In SRSWR, the number of possible sampling is
N"-52
=25
Answer: The total number of possible outcomes is 25.
Solution 2.
Here we construct the the table of all possible samples and the corresponding sample means.
Table of Sample Means
Sample values Sample mean
15000, 15000
15000
15000, 18000
16500
15000, 21000
18000
15000, 24000
19500
15000, 28000
21500
18000, 15000
16500
18000, 18000
18000
18000, 21000
19500
18000, 24000
21000
18000, 28000
23000
21000, 15000
18000
21000, 18000
19500
21000, 21000
21000
21000, 24000
22500
21000, 28000
24500
24000, 15000
19500
24000, 18000
21000
24000, 21000
22500
24000, 24000
24000
24000, 28000
26000
28000, 15000
21500
28000, 18000
23000
28000, 21000
24500
28000, 24000
26000
28000, 28000
28000
(Answer)

Solution 3.
There are 25 different possible samples, so the probability of each of the sample means is
Based on this we construct the following sampling distribution of the sample means.
Sampling Distribution of the Sample Means
Proba
Sample mean
bility
15000
1/25
16500
2/25
18000
3/25
19500
4/25
21000
3/25
21500
2/25
22500
2/25
23000
2/25
24000
1/25
24500
2/25
26000
2/25
28000
1/25
Total
(Answer)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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