Here is the some sample questions along with their answers to give you an idea of the types of questions that may be asked in such exams:
1. Descriptive Statistics:
- Question: What is the median of the following data set? {12, 18, 20, 25, 30} Answer: Median = (20 + 25) / 2 = 22.5
2. Probability Theory:
- Question: If P(A) = 0.4 and P(B) = 0.3, what is P(A ∩ B) if A and B are independent events? Answer: P(A ∩ B) = P(A) * P(B) = 0.4 * 0.3 = 0.12
3. Statistical Inference:
- Question: A manufacturer claims that the average lifespan of its product is 5 years with a standard deviation of 1 year. What is the probability that a randomly selected product will last more than 6 years? Answer: Using the z-score formula, z = (X – μ) / σ, z = (6 – 5) / 1 = 1. Therefore, the probability is approximately 0.1587.
4. Regression Analysis:
- Question: Given the simple linear regression equation y = 2x + 3, what is the predicted value of y when x = 5? Answer: y = 2(5) + 3 = 13
5. Sampling Techniques:
- Question: In a simple random sample of 100 students, what is the probability of selecting exactly 10 female students if 40% of the students are female? Answer: Using the binomial probability formula, P(X = k) = (n choose k) * p^k * (1 – p)^(n – k), P(X = 10) = (100 choose 10) * (0.4)^10 * (0.6)^90
Please note that these are just sample questions and answers to illustrate the types of topics covered in a statistics exam. Actual questions in the TNPSC Statistics exam may vary in difficulty and format. It’s essential to thoroughly study the syllabus and practice with previous years’ question papers to prepare effectively for the exam.
