Q1. State whether the following statements are true or false and also give the reason in support of your answer:
- (a)) The total number of all possible samples of size 2 without replacement from a population of size 7 is 21. (100 words)
- (b)) Consecutive 3 random numbers starting from 8937 by 'middle square method' are 8937, 8699, 6726. (100 words)
- (c)) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks. (100 words)
- (d)) As we increase the sample size, representativeness of the population by the sample decreases. (100 words)
- (e)) In a big hall, there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15 students from each selected row. It is an example of cluster sampling procedure. (100 words)
Key Points:
- Combinations (C(N, n)) calculate samples without replacement where order doesn't matter.
- Middle Square Method generates pseudo-random numbers by squaring and extracting middle digits.
- Randomized Block Design (RBD) requires homogeneous blocks to control variability.
- Larger sample sizes generally increase representativeness of the population.
Answer: This response systematically evaluates five statistical statements, determining their truthfulness and providing comprehensive justifications based on core concepts from the MST-005 'Statistical Techniques' course. Each sub-question delves into fundamental areas such as sampling theory, random number generation, and experimental design, offering detailed explanations and calculations where applicable. The analysis draws upon standard definitions and methodologies taught in the course, ensuring ...