FIRST PART Conduct an investigation considering the following concepts: Include numerical examples for a better understanding of the concepts. Nonparametric statistics Goodness of fit Chi-square...

HOME WORK    
HOME WORK    
HOMEWORK
Table of Contents
Response to Questions    2
FIRST PART    2
SECOND PART    3
Q1.    3
Q2.    5
Response to Questions
FIRST PART
· Statistical inferences where decisions are not concerned with the value of one or more parameters are termed nonparametric, whereas those inferences whose validity does not depend on a specific probability model in the population are termed distribution-free. Though these two terms are not synonymous, procedures of either type are known as nonparametric methods.
· Chi-Square goodness of fit test is employed to compare between the observed and expected frequencies to determine whether observed results are in accordance with a stated null hypothesis.
· Chi-square distribution is also employed to test the independence and homogeneity of the data set.
· But the chi-square distribution is difficult apply when the class frequency is less than 5, to apply this, the classes have to be merged.
· Also, chi-square test cannot be applied when the data is ordinal in nature.
· For, example a paint manufacturing company wants to give its customer wider choice, but at the same time does not want to produce shades, which are of little demand. Initially , the company started with only four different shades – very light, light, medium and dark. Let us suppose, that company wants to hire an employee to resolve this problem. Actually, the company wants to determine whether any distinct preferences exists toward either extreme. If so, the company wants to manufacture only the preferred shades. Otherwise it is planning to market all shades. Let us assume that the sample data shows that out of 100 customers, 10 preferred the very light shade, 30 the light shade, 15 the medium shade and 5 the dark shade.
For this type of data, Kolmogorov –Simrov test can be applied instead of Chi-square test.
Kolmogorov–Smirnov test (K–S test) is a nonparametric test for the equality of continuous probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test). The Kolmogorov–Smirnov statistic quantifies a distance between the empirical cumulative distribution function (of the sample) and the cumulative distribution function of the assumed distribution, or between the empirical...