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Hyp B

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  ?