Report on Simple Random Sampling with or without replacement

One of my friend has a problem on simple random sampling. Can someone provide a complete Report on Simple Random Sampling with or without replacement?

E

Expert

Verified

Abstract:

This project investigates selected sampling methods and their performance is tested under artificial population. Using a finite population size of 500 and a sample size of 30, estimators of first moment of the true population are compared and discussed. It is found that simple sampling method performed better in terms of precision in the analysis.

Introduction:

This project aims at comparing various sampling methods used in survey and experimental design. This project will proceed as follows. Two sampling methods are chosen to be compared in this project. Sampling procedures and descriptions of these two selected sampling methods are discussed in the next section of the project. The third section discussed the estimation theory on the population mean in the sample, with and without knowing the priori information in the sample. The third section applies the sampling method numerically. Point estimates on first and second moments of will be provided in this section. The forth section discusses the bias of the sampling methods based on the assumption that the true population mean is known beforehand.

Sampling Methods:

The sampling methods used in this project are (1) Simple Random Sampling Without Replacement and (2) Simple Random Sampling With Replacement.

One of the simplest probability sampling designs (plans) to select a sample of fixed size n with equal probability, i.e. 0 otherwise. One way to select such a sample is use Simple Random Sampling Without Replacement (SRSWOR): select the 1st element from U = {1, 2, • • • ,N} with probability 1/N; select the 2nd element from the remaining N −1 elements with probability 1/(N −1); and continue this until n elements are selected. Let {yi, i 2 s} be the sample data. It can be shown that under SRSWOR, otherwise. In practice, the scheme can be carried out using a table of random numbers or computer generated random numbers.

The simple random sampling with replacement can be described as below. First, the 1st element is selected from the sample with size N where the sample is labeled as {1,2,…,N} with equal likelihood, then we repeat this step n times to draw the required n samples from the sample. It should be noted that some elements in the population can be drawn more than once. Using the definition in the previous part, the mean estimates of the population using the sample can be computed as:

The strengths of both SRSWOR and SRSWR are (1) they are both simple sampling methods; (2) they are easy to be implemented for large sample size without huge computation power. However, compared to other sampling methods, these two methods suffer from the precision of the estimates. Comparing with other sampling methods, these two methods require additional sample size in order to give similar precision as other methods. Therefore, if the sample size is small in the sample, the precision of estimates will be affected.

To know more..

Related Questions in Basic Statistics

• Q :Assumptions in Queuing system

Assumptions in Queuing system:

Flow balance implies that the number of arrivals in an observation period is equal to the

• Q :How to solve statistics assignment in

How to solve staistics assignment, i need some help in solving stats assignment on AVOVA based problems. Could you help in solving this?

• Q :Get Solved LP Problems Solve Linear

Solve Linear Programming Questions

A producer manufactures 3 models (I, II and III) of a particular product. He uses 2 raw materials A and B of which 4000 and 6000 units respectively are obtainable. The raw materials per unit of 3

• Q :Variance and standard error A hospital

A hospital treated 412 skin cancer patients over a year. Of these, 197 were female.

Give the point estimate of the proportion of females seeking treatment for skin cancer.

Give estimates of the

• Q :Quantities in a queuing system

Quantities in a queuing system:

A: Count of

• Q :FIN512 Entrepreneurial Finance Chapter

Chapter 6: Discussion Question: #4 p. 223

It is usually easier to forecast sales for a seasoned firm contrast to an early-stage venture because an early-stage venture has limited access to bank credit lines, sho

• Q :Safety and Liveness in Model Checking

Safety and Liveness in Model Checking Approach;

•? Liveness: Something good happens

•? Model checking is especially good at verifying safety and liveness properties
–?Concurrency i

• Q :Sample Questions in Graphical Solution

Solved problems in Graphical Solution Procedure, sample assignments and homework

Questions: Minimize Z = 10x1 + 4x2

Subject to

• Q :Simplified demonstration of Littles Law

Simplified demonstration of Little’s Law:

Q :Stats The College Board SAT college

The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012). Sample data showing the math and writing scores for a sample of twelve students who took the SAT follow. http://west.cengagenow.com/ilrn/books/assb12h/images/webfiles/