NTA UGC NET _ Commerce - Unit 5: Business Statistics and Research Methods (PART 02)

 

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Unit 5

Business Statistics and Research Methods

PART 02

 

MCQ 01: Goodness of fit of a distribution is tested by
 

a) t-test
b) chi-square test
c) f-test
d) None of the above
 

Ans: chi-square test

 

Chi-square test
 

_Non parametric test

 

_Introduced by Karl Pearson

 

 

 

 

 

 

 

 

 

 

 

_Used to Test :

•     the discrepancies between observed and expected frequencies

•     goodness of fit

•     determine association between two or more attributes

 

 

 

 

 

 

 

 

Based on frequencies

 

Assumptions :

•     All the observations must be independent

•     All the events must be mutually exclusive

•     There must be large observations (50)

•     The data must be in original units

•     Properties of Chi- square Distribution

t- test (Student's T Distribution ) 

 

It is used to check whether two data sets are significantly different from each other or not.

 

• one-sample t-test

 

 

 

 

 

 

 

 

 

where

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• Two-sample t-test

Where, 

 

 

 

 

 

s1 = Standard Deviation of 1st Sample
s2= Standard Deviation of 2nd Sample
n 1 = Size of 1st Sample
n 2 = Size of 2nd Sample

 

• Parametric test

• Population S D unknown

• Sample size small (max 30)

• Normal bell shaped curve (symmetrical around the mean 0)

• ranges from –∞ to ∞ (infinity). 

f-test

• to test if two population variances are equal

• if the variances are equal, the ratio of the variances will be 1

• F-test is also a small sample test.

• F-distribution depends on the degrees of freedom

• also called as Variance Ratio Distribution.

• The F-distribution is positively skewed

• F-distribution is always positive, or zero (Its value lies between 0 and ∞.)

• Shape depends on degree of freedom

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