Q1. State whether the following statements are true or false and also give the reason in support of your answer:
- (a)) If X1, X2, X3, ..., Xn and Y1, Y2, Y3, ..., Yn are the variate values of two variables X and Y, and their geometric means are G1 and G2, respectively, then geometric mean of (xj/yi); i = 1, 2, ... n will be (G1/G2). (100 words)
- (b)) If X and Y are two independent variables and the variables U = X+ Y and V=X-Y, then the r(U, V) = +0 (100 words)
- (c)) If each value of X is divided by 2 and of Y is multiplied by 2, then b'yx will be same as b. (100 words)
- (d)) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%. (100 words)
- (e)) If (A) = 90, (AB) = 40, N = 150 and (β) = 80 then (αβ) = 30. (100 words)
Key Points:
- Geometric Mean of a ratio of variables is the ratio of their GMs.
- Correlation between (X+Y) and (X-Y) for independent X, Y is (Var(X)-Var(Y))/(Var(X)+Var(Y)).
- Regression coefficients are sensitive to changes in scale, multiplying by factors.
- Adding a constant to data changes mean but not standard deviation.
Answer: