Match the items of List I with the items of List-II and select the correct answer: List-I List-II a. Contingency coefficient for any size of contingency table 1. $$\sqrt {\frac{{N – n}}{{N – 1}}} $$ b. Statistical approach to decide size of a sample 2. $$\frac{{{\sigma _p}}}{{\sqrt n }}$$ c. Finite population multiplier 3. $$\sqrt {\frac{{{x^2}}}{{{x^2} + n}}} $$ d. Standard error of mean 4.$$\frac{{{Z^2} \cdot \sigma _p^2}}{{{e^2}}}$$

The correct answer is: A. a-1, b-2, c-3, d-4

Here is a brief explanation of each option:

• a. Contingency coefficient for any size of contingency table: This is a measure of the strength of the association between two categorical variables. It is calculated as follows:

$$C = \sqrt {\frac{{X^2}}{{X^2} + n}}$$

where $X^2$ is the Pearson’s chi-square statistic and $n$ is the sample size.

• b. Statistical approach to decide size of a sample: This is a method for determining the sample size required to achieve a desired level of precision in estimating a population parameter. The most common approach is to use the following formula:

$$n = \frac{Z^2 \cdot \sigma_p^2}{{{e^2}}}$$

where $Z$ is the z-score corresponding to the desired level of confidence, $\sigma_p$ is the standard error of the population parameter, and $e$ is the desired margin of error.

• c. Finite population multiplier: This is a factor that is used to adjust the standard error of the mean when the sample is taken from a finite population. It is calculated as follows:

$$f = \sqrt {\frac{{N – n}}{{N – 1}}}$$

where $N$ is the population size and $n$ is the sample size.

• d. Standard error of mean: This is a measure of the variability of the sampling distribution of the mean. It is calculated as follows:

$$\sigma_m = \frac{{\sigma_p}}{{\sqrt n }}$$

where $\sigma_p$ is the standard deviation of the population and $n$ is the sample size.