CSIR NET Maths previous year question papers

Suppose we want to estimate the population mean Ȳ of a variable for a finite population of size 85, with 34 Statisticians and 51 Biologists. We consider the following sampling scheme: a stratified random sample with 2 strata of Statisticians (Stratum-1) and Biologists (Stratum-2), where 12 Statisticians and 15 Biologists are drawn from Stratum-1 and Stratum-2, respectively, using SRSWOR scheme. Denote ȳ_S, ȳ_B, and ȳ as the mean of the variable among the Statistician sample, Biologist sample, and the combined sample, respectively. Which of the following is an unbiased estimator of Ȳ?

Consider a finite population of size N = 100. Let $T_{1}$ be the sample mean of a study variable based on a sample of size n (1 < n < N) under simple random sampling with replacement scheme. Let $T_{2}$ be the sample mean of the same study variable based on a sample of size n under simple random sampling without replacement scheme. If $Var(T_{1}) = 9Var(T_{2})$, then the sample size n equals

If the incidence matrix of a block design is given by N with rows (1, 1, 1, 0), (1, 1, 0, 1), (1, 0, 1, 1) and (0, 1, 1, 1), then which of the following statements are true?

Consider a dataset of n observations given by A = {$x_{1},x_{2},\dots,x_{n}$}. Create a new dataset, given by B = {$x_{1},x_{2},\dots,x_{n},-x_{1},-x_{2},\dots,-x_{n}$}. Which of the following statements are always true? (Variance is calculated with divisor as the number of observations in the corresponding dataset.)

Consider the following $2^{5}-$factorial design with 8 blocks (Block 1: (1), acd, bce, abde; Block 2: e, acde, bc, abd; and six further blocks). Which of the following statements are true?

Consider the following design where the columns represent blocks and the letters represent treatments — block 1: A, B; block 2: C, D; block 3: A, C; block 4: B, D; block 5: A, D; block 6: B, C; block 7: A, E; block 8: B, E; block 9: C, E; block 10: D, E. Then, which of the following statements is NOT true?

Let P be the population proportion of units possessing a certain attribute in a population of N units. Let p be the sample proportion in a simple random sample (without replacement) of n units, (2 ≤ n < N). Then an unbiased estimator of P(1 − P) is

The expected number of distinct units in a simple random sample of 3 units drawn with replacement from a population of 100 units is

Consider a probability proportional to size without replacement sample involving two draws from a population of N (> 6) units with normed size measures $p_{i}'s (p_{i} > 0, i = 1, 2, \dots, N; \sum(i=1..N)p_{i} = 1)$. Then, which of the following statements are true?

Consider the following design where the columns represent blocks and the letters represent treatments — block 1: A, B, E; block 2: C, D, E; block 3: A, C, F; block 4: B, D, F; block 5: A, D, G; block 6: B, C, G; block 7: E, F, G. Then, which of the following statements are true?

Consider the following ANOVA table for a randomized block design — Treatments: sum of squares 48, degrees of freedom 4, mean squares 12, F calculated $\beta$; Blocks: sum of squares 72, degrees of freedom 3, mean squares 24, F calculated 12; Error: sum of squares $\alpha$, degrees of freedom m, mean squares $\gamma$; Total: sum of squares 144, degrees of freedom 19. Which of the following statements are true?

In a Latin square design, the degrees of freedom for the error sum of squares is 42. Then the degrees of freedom for the sum of squares due to treatments is

Consider a population of 3 units having values 2, 4 and 6. A simple random sample (without replacement) of 2 units is drawn. Let M be the sample mean. Which of the following statements are true?

Two groups $G_{1}$ and $G_{2}$ have 10 and 30 patients with mean diastolic blood pressures 80 and 100 mmHg and variances 4 and 2 mmHg$^{2}$. Let ${\bar{X}}, S^{2}, C$ and R be the mean, variance (with divisor n), coefficient of variation (%) and range of the combined group. Which of the following statements are true?