Students t distribution - hypothesis testing, Operation Research

Assignment Help:

Students  t Distribution

If we  take a very large number of small  samples  from a population  and calculate the mean for each  sample and then  plot  the frequency  distribution  of these  means the resulting sampling  distribution  would be  the students t distribution.

The  greatest  contribution to the theory  of small  sample was made by Sir  William Gossett and R. A Fisher  published his discovery in 1905 under  the pen name  the  students and it is popularly known  as test or student distribution  or student distribution.

When  the sample  size is 30  or less  the population  standard deviation is unknown  we can  use  the t distribution.

The formula  is             t  = ( X - µ) / s X √ n

Where  s or  sample standard  deviation

 

940_students  t Distribution.png

 

  if samples  S. D is given  without  using n-1 denominator then

 t= ( X- µ))/ S/ √ n-1

      it should  be noted that the  only difference in the calculation of S in large and small  samples is that  whereas  in the case of the former the sum  of the squares of deviations of  various  items  from the mean of ∑ ( X-X)2 is divided by  n-1. ( the number of items ) in  case of small  samples it is  divided by  n-1 which are  the degrees  of freedom. The  degree of  freedom in such  problems i s n-1 because one has  the freedom  to change only n-1 items as the last items has to be the difference between ∑X and the sum  of n-1 items.  Thus if  there  are 5 items  in a sample with  a total  of 30. We  can change  only 4  items as we like. The  last items will have to be  30 minus the sum  of the remaining 4items. whose  values  have been  changed.


Related Discussions:- Students t distribution - hypothesis testing

Introduction to probability distribution , Introduction to Probability Dist...

Introduction to Probability Distribution By  theoretical distribution we mean  a frequency distribution  which  is obtained  in relation to a random  variable by some  mathem

Assignment, Q2.Six Operators are to be assigned to five jobs with the cost ...

Q2.Six Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assignm

Linear programming problem, A paper mill produces two grades of paper viz.,...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Closed lood, give the procedure of tracing a closed loop

give the procedure of tracing a closed loop

Least cost method of transportation model, how do you calculate using this ...

how do you calculate using this method where the least cost appears twice

Standara deviation - measure of dispersion , STANDARA DEVIATION Standa...

STANDARA DEVIATION Standard  deviation  is the  square  root of the  arithmetic  average of  squares of all  the deviations from the  mean. In short  it may  be defined  as th

Scientific methods, Royce A. Singleton and Bruce C. Straits have said tha...

Royce A. Singleton and Bruce C. Straits have said that scientific social research consists of the process of formulating and seeking answers to question about the social wor

Fromulation of LPP, A paper mill produces two grades of paper viz., X and ...

A paper mill produces two grades of paper viz., X and Y because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons ot grade Y paper in

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd