PROBABILITY AND STATISTICS Assignment-3

 

Assignment Content

1. Question 1

   2 Points

   Fit the parabola is Y=a X^2+bX+c for the data x: 1, 3, 4 , 6 ,8 ,9, 11, 14 and y: 1,2, 4, 4, 5, 7, 8, 9.

   
   
2. Question 2

   2 Points

   A computer while calculating correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results : n=25, ∑ X= 125, ∑ X^2=650, ∑ Y=100, ∑ Y^2= 460, ∑ XY =508. If was, however, later discovered at the time of checking that he had copied down two pairs as (X,Y)= (6,14),(8,6) while the correct values were (X,Y)=(8,12),(6,8).

   Obtain the correct value of correlation co-efficient.

   
   
3. Question 3

   2 Points

   By using least square principle for fitting, fit straight line for the data X: 0,1,2,3,4 and Y: 1.0, 2.9, 4.8, 6.7, 8.6 

   
   
4. Question 4

   2 Points

   A manufacturer claims that only 4% of his products supplied by him are defective. A random sample of 600 products contains 36 defectives. Test the claim of the manufacturer.

   
   
5. Question 5

   2 Points

    12 entries in a painting competition were ranked by two judges , Judge I : 5, 2, 3, 4, 1, 6, 8, 7, 10, 9, 12, 11 and by  Judge II: 4, 5, 2, 1, 6, 7, 10, 9, 11, 12, 3, 8 . Calculate Spearman's rank correlation coefficient.