The question requires matching statistical terms in List – I with their corresponding formulas or approaches in List – II.

Analyzing the Matches

i. Contingency Coefficient

The contingency coefficient is a measure of association between two observed frequency distributions. For any size contingency table, it is calculated using the chi-square ($\chi^2$) statistic and the total number of observations ($n$). The formula is: $C = \sqrt{\frac{\chi^2}{\chi^2 + n}}$ This matches item c in List – II.

ii. Statistical Approach for Sample Size

Determining the appropriate sample size ($n$) involves statistical considerations such as the desired margin of error ($e$), the confidence level (represented by $z$), and the population variance ($\sigma_p^2$). A common formula used is: $n = \frac{z^2 \cdot \sigma_p^2}{e^2}$ This matches item d in List – II.

iii. Finite Population Multiplier

When sampling without replacement from a finite population, the variance and standard error are adjusted using the finite population multiplier. If $N$ is the population size and $n$ is the sample size, the multiplier is: $\sqrt{\frac{N - n}{N - 1}}$ This matches item a in List – II.

iv. Standard Error of Mean

The standard error of the mean (SEM) quantifies the variability of sample means around the population mean. It is calculated using the population standard deviation ($\sigma_p$) and the sample size ($n$): $SE(\bar{x}) = \frac{\sigma_p}{\sqrt{n}}$ This matches item b in List – II.

Conclusion

Based on the analysis, the correct matching is:

• i matches with c
• ii matches with d
• iii matches with a
• iv matches with b

Therefore, the correct code is i-c, ii-d, iii-a, iv-b.