Simple Random Sampling (SRSWR, SRSWOR), Stratified Sampling & Allocation Methods

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