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…

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.

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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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 Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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