For estimating population mean {Y} of a study variable Y using... | Agrigyan

91
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct)
Identify the best test to be adopted for testing the equality of mean thrips incidence in a set of same samples before and after spray of a treatment
92
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct)
Indicate the distribution free method used for testing K matched samples based on ordinal level of measurement
93
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct)
Non parametric measure of association used in case of categorical level of measurement is
94
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct)
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
95
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct)

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:

1. $\left(\frac{1}{n} - \frac{1}{n'}\right) S_x^2$
2. $\left(\frac{1}{n'} - \frac{1}{N}\right) S_x^2$
3. $0$
4. $\left(\frac{1}{n} - \frac{1}{N}\right) S_x^2$

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