Explore BrainMass
Share

Word Problems - Studying Statistics : Law of Large Numbers and Sampling Techniques

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

1. Explain in your own words the law of large numbers. Provide an example to illustrate.

2. Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1.

3. Why is expectation important? Explain what the expected value of an experiment or a business represents. What does it mean to have an expected value of 0? Provide an example of expectation and the use of the formula for expected value.

1. What are the reasons for studying statistics?

2. From your readings, select a sampling technique of your choice. Describe how the technique can be used to obtain the type of sample. Indicate when the technique may be preferred. List two examples of when the sampling technique may be used.

© BrainMass Inc. brainmass.com October 24, 2018, 9:02 pm ad1c9bdddf
https://brainmass.com/math/basic-algebra/word-problems-studying-statistics-law-of-large-numbers-and-sampling-techniques-114689

Solution Preview

1. Explain in your own words the law of large numbers. Provide an example to illustrate.

The law of large numbers is a fundamental concept in statistics and probability that describes how the average of a randomly selected large sample from a population is likely to be close to the average of the whole population. The term "law of large numbers" was introduced byS.D Poisson in 1835 as he discussed a 1713 version of it put forth by James Bernoulli.[1]
In formal language:
If an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions converges towards p as the number of repetitions becomes arbitrarily large.
In statistics, this means that when a large number of units of something is measured, the sample's average will be close to the true average of all of the units?including those that were not measured. (The term "average" means the arithmetic mean.)
There are two versions of the Law of Large Numbers, one called the "weak" law and the other the "strong" law. This article will describe both versions in technical detail, but in essence the two laws do not describe different actual laws but instead refer to different ways of describing the convergence of the sample mean with the population mean. The weak law states that as the sample size grows larger, the difference between the sample mean and the population mean will approach zero. The strong law states that as the sample size grows larger, the probability that the sample mean and the population mean will be exactly equal approaches 1.
The phrase "law of large numbers" is also sometimes used in a less technical way to refer to the principle that the probability of any possible event (even an unlikely one) occurring at least once in a series increases with the number of events in the series. For example, the odds that you will win the lottery are very low; however, the odds that someone will win the lottery are quite good, provided that a large enough number of people purchased lottery tickets.
One misperception of LLN is that if an event has not occurred in many trials, the probability of it ...

Solution Summary

Studying Statistics, the Law of Large Numbers and Sampling Techniques are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19
See Also This Related BrainMass Solution

Descriptive and Inferential Statistics: Consulting Firms

See attached files.

1. Differentiating Descriptive and Inferential Statistics

Resource: Iwamoto.Crews.Coe Virtual Organization portal

Access the ICC.zip file and select the Iwamoto.Crews.Coe consulting firm. Various companies have hired the firm to handle matters of organizational development, professional growth, and marketing. Go to the Iwamoto.Crews.Coe intranet site and review the following business problems:

o Organizational Development
Benedek Medical Technologies, Inc. - Knowledge Test Design
Haynes Medical Distribution - Employee Retention
Riordan Manufacturing - Leadership Traits

o Professional Growth
Loehr Equipment Co. - E-Learning Study

Review the information provided in the description of each business problem and identify which of the problems an Industrial / Organizational Psychologist would want to use descriptive statistics and which of the problems he/she would want to use inferential statistics.

Provide a paper that discusses the following:

o How descriptive statistics differ from inferential statistics and when it is appropriate to use each
o Key similarities and differences among the four business problems and how these similarities and differences influenced your decisions regarding the use of descriptive and inferential statistics

Submit the paper as a Microsoft Word attachment to your Individual forum.

View Full Posting Details