Correlation means
A.  The whole subject of correlation refers to that interrelation between separate character by which they tend, in some degree at least, to move together. 
B.  That between two series or groups of data there exists some caustional connections. 
C.  Whenever some definite connections exist between the two or more groups, classes or series to data, there is said to be correlation. 
D.  All of the above. 
Option: D Explanation : 
Match the following
ListI (Items)
(A) Probability
(B) z = (x — μ)/σ
(C) t test
(D)
ListII (Application)
1. Event
2. Distribution
3. Hypothesis test
4. Normal distribution
A.  (A) (B) (C) (D) 1 2 3 4 
B.  (A) (B) (C) (D) 3 1 4 2 
C.  (A) (B) (C) (D) 4 1 3 2 
D.  (A) (B) (C) (D) 1 4 3 2 
Option: A Explanation : 
If r_{12} = 0.86, r_{13} = 0.65 and r_{23} = 0.72, prove that r_{12.3} = 0.743
A.  0.32 
B.  0.743 
C.  0.31 
D.  0.740 
Option: B Explanation :
Hence the answer is (b). 
In a random sample of 100 people, 40% of them are nonvegetarian. What proportion of the whole population is nonvegetarian?
A.  54.3% 
B.  36.9 to 37.9% 
C.  30.6% 
D.  54.7% to 25.3% 
Option: D Explanation : P = 40/100 = 0.4 q = 1  p or 0.6 = 1  0.4 Standard error = √npq = √(100 x 0.4 x 0.6) = √24 = 4.899 3 x 4.899 ± 40 = 54.7 to 25.30% are nonvegetarian, Hence the answer is (d).

In a sample of 400 books 172 were Economics books. Estimate the population proportion at 95% confidence levels
A.  9% to 12% 
B.  12% to 43% 
C.  47.86% to 38.14% 
D.  43% to 12% 
Option: C Explanation : Sample proportion = 172/400 = 0.43 or p= 0.43 or q = 1  p 0.57 = 1 0.43 σ = √pq/n = √(0.43 x 0.57)/400 = 0.0248 Population proportion at 95% confidence level = Sample proportion ± 1.96 σ = 0.43 ± 1.96 x 0.0248 = 0.43 ± 0.0861 = 0.47861 to 0.38139 or between 47.86 to 38.14%. Hence the answer is (c). 