Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 5: Q45E (page 230)
Carry out a simulation experiment using a statistical computer package or other software to study the sampling distribution of \({\rm{\bar X}}\) when the population distribution is lognormal with \({\rm{E(ln(X)) = 3}}\) and\({\rm{V(ln(X)) = 1}}\). Consider the four sample sizes\({\rm{n = 10,20,30}}\), and\({\rm{50}}\), and in each case use \({\rm{1000}}\) replications. For which of these sample sizes does the \({\rm{\bar X}}\) sampling distribution appear to be approximately normal?
Short Answer
The last histogram and normal probability plot are for sample size\({\rm{n = 300}}\), mainly to show that the sample distribution becomes closer to normal as \({\rm{n}}\) rises.
Step by step solution
Definition
Probability simply refers to the likelihood of something occurring. We may talk about the probabilities of particular outcomes鈥攈ow likely they are鈥攚hen we're unclear about the result of an event. Statistics is the study of occurrences guided by probability.
Determining the sample size
Simulate the sample distribution of \({\rm{\bar X}}\) using any programmed, such as \({\rm{R}}\), math lab, python, or a statistical computer package, given a lognormal distribution with expectation \({\rm{3}}\) and variance\({\rm{1}}\).
Calculate the mean for each sample first. A histogram and a normal probability plot should be plotted. The distribution tends to be normal as \({\rm{n}}\) rises; nevertheless, as the histograms and normal probability plots below show, the distribution is not roughly normal for given sample sizes. The last histogram and normal probability plot are for sample size\({\rm{n = 300}}\), mainly to show that the sample distribution becomes closer to normal as \({\rm{n}}\) rises.
For\({\rm{n = 10}}\), the following are histogram and normal probability plot:
Determining the sample size
\({\rm{ For n = 20, the following are histogram and normal probability plot: }}\)
Determining the sample size
\({\rm{ For n = 30, the following are histogram and normal probability plot: }}\)
Determining the sample size
\({\rm{ For n = 50, the following are histogram and normal probability plot: }}\)
Determining the sample size
\({\rm{ For n = 300, the following are histogram and normal probability plot: }}\)
Over 30 million students worldwide already upgrade their learning with 91影视!
