Design of Experiments

Of the 36 accounts drawn randomly from a very large number of accounts in a certain bank, 12 had a deposit of less than Rs. 1500. The estimated standard error for the estimate of the proportion of accounts having a deposit of less than Rs. 1500 is

‘Two samples of size n ate selected, one according to SRSWR and the other according to SRSWOR. Under SRSWR, V; stands for variance of sample mean based on all units while V2 stands for the variance of sample mean based on distinct units. V3 stands for the variance of sample mean based on SRSWOR. Which one of the following holds ?

Asimple random sample of 4 households was drawn from a village containing 120 households. The number of persons per household in the sample were 6, 4, 7 and 3. The estimate of the total number of people in the village is

In drawing a sample of size n from a finite population of size N using Simple Random Sampling With Replacement (SRSWR), the probability that a specified unit is included in the sample is

A sample of 100 employees is to be drawn from a population divided into two strata. The strata population sizes $N_i$, population means (Pop. $M_i$) and the population mean squares (Pop. $MS_i$) of their monthly wages are given below:

Then the sample sizes using proportional and Neyman allocations are given by:

Based on past experience, it is known that standard deviation of weight of one year old rohu fish is 25 g. If it is decided to estimate mean weight within 5 units of true value in either direction with confidence coefficient of 0.95 (note that the standard normal variate Z takes the value 1.96 ~ 2 approximately, at this 95% confidence level), then if the sampling is done with SRSWR and that the finite population correction is ignored, the required sample size is approximately

Which one of the following is an example of primary database?

Thomson Reuters was created by the Thomson Corporation's purchase of the --------------company, Reuters Group.

Consider the population U = {1, 2, 3} with P({1, 2}) = 1/2; P((1, 3}) = 1/4; P({2, 3}) = 1/4. Then if 1% denotes the first order inclusion probability of the k-th unit (k=1, 2, 3), which of the following is NOT true’

Avillage has 10 orchards numbered 1 to 10 containing 150, 50, 80, 100, 200, 160, 40, 220, 60, 140 trees respectively. It is desired to select a sample of 4 orchards PPS With Replacement to the number of trees in the orchard. By cumulative total method, if the random numbers chosen in the successive draws are 600, 650, 850 and 300,

For estimating population mean $\bar{Y}$ of a study variable $Y$ using double sampling, information on an auxiliary variable $X$ was collected from a large preliminary sample of size $n'$ units of a population in which $X$ alone was measured to furnish an estimate $\bar{x}'$ of population mean of $X$, as the information about $X$ of the population was not readily available. From this large preliminary sample, a smaller sample of size $n$ was selected and the information on the main variable $Y$ was collected and sample mean $\bar{y}$ and corresponding sample mean $\bar{x}$ were computed. In both phases, SRSWOR was done. The estimates were then used to obtain a ratio estimator $\bar{y}_d = \frac{\bar{y}}{\bar{x}} \bar{x}'$. While deriving the variance of this ratio type mean estimator, the following errors were considered: $e_1 = \frac{\bar{x} - \bar{x}'}{\bar{X}}$ and $e_2 = \frac{\bar{x}' - \bar{X}}{\bar{X}}$. Then, if $S_x^2$ is the population variance of $X$, $E(e_1 e_2)$ is:

Consider the problem of estimating the total number of palm trees on 100 islands in a tropical paradise. The area of each island is known and it is reasonable to think that the number $y_i$ of palm trees on each island is approximately proportional to the size of the island. The total size of these 100 islands is 100 square miles. Let the units selected with replacement in 4 independent draws be the islands numbered 1, 29, 36 and 29 with information details as follows:

Then the Horvitz-Thompson estimate for estimating the total number of trees is:

Consider the following statements to estimate the total marine fish landings of our country:

Consider the following statements:

Choose the correct answer from the options given below: