State whether the following statements are true or false. Give a brief justification.
a) If two variables are independent, then the coefficient of correlation between them
is 1.
b) The mean of a binomial distribution is 10 and the standard deviation is 4.
c) Simple random sampling is done by using a random number where the probability of
drawing a digit is 0.1.
d) The number of six-digit telephone numbers generated with distinct digits is (9)⁶.
e) If 25 is subtracted from each value of X and Y and then divided by 10, the new b'ᵧₓ is 2.5 times of bᵧₓ, where bᵧₓ is a regression coefficient of Y on X.
Answers
Step-by-step explanation:
a,False
If the variables are independent, correlation coefficient is 0
b,not sure about this
c,T
d,T
e,not sure
a) false
b) true
c) true
d) false
e) true
a)
If two variables are independent, then the coefficient of correlation between them is 0.
Therefore, the given statement is false.
b)
np = 10
np (1 - p)=2
10 (1 - p) = 2
5 (1 - p) = 1
1 - p = 1/5
p = 1 - 1/5 = 4/5
Therefore, the given statement is true.
c)
The string of digits we write constitutes a string of random digits because it has been produced by a random device expected to generate each digit with a probability of 0.1 in independent trials.
supposed to yield each digit with probability 0.1 in independent trials.
Therefore, the given statement is true.
d)
First digit of the telephone number can be filled in 9 ways i.e, first digit can be 1, 2, 3, 4, 5, 6, 7, 8, 9
Second digit of the telephone number can be filled in 10 ways i.e, second digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Similarly, third, fourth, fifth and sixth digits of the telephone number can be filled in 10 ways , 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Thus, total ways can be obtained as -
1st digit in 9 ways, and rest all in 10 ways. So,9 × 10 × 10 × 10 × 10 × 10 = 900000.
Therefore, the statement is false.
e)
The number of units that Y changes when X changes 1 unit. If the slope is 2, then when X increases 1 unit, Y increases 2 units. If the slope is -.25, then as X increases 1 unit, Y decreases .25 units.
Therefore, the statement is true.