Given below are two statements:

Statement I: Sampling where each member of the population cannot be chosen more than once is called 'sampling with replacement'.

Statement II: Sampling where each member of the population may be chosen more than once is called 'sampling without replacement'.

In the light of the above statements, choose the correct answer from the options given below:

The correct answer is Both Statement I and Statement II are false.

Key Points The given statements are reversed in terms of the correct definitions.

Statement I: Sampling where each member of the population cannot be chosen more than once is called 'sampling with replacement'.

• In sampling with replacement, each member of the population has the possibility of being chosen more than once. This means that after a member is selected, they are returned to the population, and they have a chance of being selected again.

Statement II: Sampling where each member of the population may be chosen more than once is called 'sampling without replacement'.

• In sampling without replacement, each member of the population can be chosen only once. Once a member is selected, they are not returned to the population, and they are excluded from further selection.

So, Statement I should refer to 'sampling without replacement', and Statement II should refer to 'sampling with replacement'.

Hence, the correct answer is Both Statement I and Statement II are false.