Question

True or False

1. Simple random sampling will ensure a representative sample.

2. The whiskers on a box plot extend to the smallest and largest data pieces.

3. Variance can never be smaller than its standard deviation.

4. If a random variable, X, has the values x=2, 3, 4, 5 or 6 and P(x) = 0.05x then P(2<x<= 5) = 0.7

Answer 1

1) Simple random sampling ensures that each element in the population has an equal probability of being selected. Therefore it ensures a representative sample.

Therefore the given statement is TRUE .

2) The whiskers start at the minimum value and ends at the maximum value.

Therefore the given statement is TRUE .

3) Variance is computed as the square of standard deviation.

For standard deviation < 1, the variance would be less than the standard deviation.

4) P(X = x) = 0.05x

Therefore, we get here:

P(X = 2) = 0.1
P(X = 3) = 0.15
P(X = 4) = 0.2
P(X = 5) = 0.25
P(X = 6) = 0.3

Therefore, P(2 < x <= 5) = P(X = 3) + P(X = 4) + P(X = 5) = 0.15 + 0.2 + 0.25 = 0.6 which is not equal to 0.7

Therefore the given statement is FALSE .