Hyp B
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Hyp B

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Hyp B Hyp B Presentation Transcript

  •  
  • THE t DISTRIBUTION DEFINITION The t distribution is a theoretical probability distribution. It is symmetrical, bell-shaped, and similar to the standard normal curve. It differs from the standard normal curve, however, in that it has an additional parameter, called degrees of freedom, which changes its shape.
  • Student t- distribution We knows the significant of the difference between the mean of the sample and the mean of the population t = x-   /  n
  • If the S.D is not known we have to estimate it from the sample .
    • If s is the S.D of the sample is known then the Standard Error is s/  n.
    • t = x- 
    • s/  n -1 if n is small(i.e. n <=25)
    • Here we will take n-1 degrees of freedom for finding the significance level(if n is small)
  • Testing of mean population on the basis of Small and Large Samples
    • If  is known we will take the value of  in the standard normal distribution table
    • If  is not known and n is small we will take the value of n-1 (degrees of freedom) in the standard normal distribution table.
    • If n value is high in both the situation we will take value from  only
  • If the sample is large the test is Z test
    • z = x- 
    •  /  n
    • Here we will take  degrees of freedom for finding the significance level
  • Problems
    • In a production process ,the target value of  is 50 and  is not known. The sample measurement on a day are 45,54,51,47,52,50,41,51,43 and 53.Test H0:  =50 against H1:  <50 with ∞=.05) Ans: t=-.924,s=4.45
    • D.O.F=n-1 = 9 is 1.833 So rejection region is R:t<=-1.833 The value of t comes under acceptance region.i,e H0 is accepted at 5% level of significance.
    • Student’s t-distribution- one tail test
    • (Q.T by Srivastava
    • -1.833
  • Problem 2
    • The kairali restaurant has been arranging sales of 300 lunch packets per day at Brigade road. Because of the construction of the new building and other complexes , it expects to increase the sale. During the first 16 days after the occupation of these building ,the daily sales were 304,367,385,386,262,329,302,292,350,320,298,258,364,294,276 and 333. On the basis of this information will you conclude that Kairali’s sales have increased.
    • Ans.Let x be the daily sales
    • H0 is  <=300(We consider the sales have not increased unless proved)
    • H1 is  >300
    • t=1.94
    • R:t>=1.75 t(.05,15) n-1=15 Two tail Test
    • We reject the hypothesis
    • .05
    • 1.75
  • Home work
    • A certain stimulus administered to each of 10 patients resulted in the following increases of blood pressure.8,8,7,5,4,1,0,0,-1,-1. Can it be concluded that the stimulus was responsible for the increase in blood pressure.
    • Ans: H0:  =  0 H 1:  0
    • s=3.53
    • t =2.63
    • D.o.f=9 ,
    • .
      • . 025 .025
    • -2.26 2.26
  • Homework
    • Illustration 1: A manufacturer of vitamin B-complex tables wants to check the quality of his product. on the basis of his experiences, he has estimated mean content (  ) of a batch as 100 units and the standard deviation as 10 units. For a new batch, if he tests 25 tables, what will be the distribution for the sample mean  ?
    •