Question

Which of the following is/are true? A. Correlation coefficient always lies in \([-1,1]\).
B. Mean, Mode and Median are always equal when data follows normal distribution.
C. Mean, Mode and Median are always equal when data follows binomial distribution with odd number of sampling points.
D. Researchers generally reject the null hypothesis when \(p\)-value is less than \(0.05\).

• A. A only
• B. A, B and D only
• C. A, B and C only
• D. A, B, C and D only

Hint:

For normal distribution, mean, median and mode are equal. In hypothesis testing, \(p<0.05\) usually leads to rejection of \(H_0\).

Answer 1

The Correct Option is B

Concept:
This question is based on correlation, normal distribution and hypothesis testing.

Step 1: Check A.
Correlation coefficient always lies between \(-1\) and \(1\): \[ -1\leq r\leq 1 \] So, A is true.

Step 2: Check B.
For normal distribution: \[ \text{Mean}=\text{Median}=\text{Mode} \] So, B is true.

Step 3: Check C.
For binomial distribution, mean, median and mode are not always equal. This depends on the parameters. So, C is false.

Step 4: Check D.
If \(p<0.05\), researchers generally reject the null hypothesis at \(5\%\) level of significance. So, D is true. \[ \therefore \text{Correct Answer is (B)} \]