Given below are two statements:

Statement I: Time and cost are not relevant in determining the sample size

Statement II: Unit non-response and item non-response do not matter in deciding the sampling error.

In the light of the above statements, choose the correct answer from the options given below.

The correct option is Both Statement I and Statement II are false.

Let us analyze the validity of each statement step-by-step to understand why both are incorrect.

Analysis of Statement I: "Time and cost are not relevant in determining the sample size"
In practical research and survey design, time and cost are among the most critical constraints. A larger sample size generally provides more precise results and reduces the margin of error, but it requires significantly more financial resources, labor, and time to collect and process the data. Therefore, researchers must always balance the desired statistical precision against the available budget and time limits. This makes time and cost highly relevant in determining the sample size, rendering Statement I false.

Analysis of Statement II: "Unit non-response and item non-response do not matter in deciding the sampling error."
Non-response occurs when selected respondents do not participate (unit non-response) or do not answer specific questions (item non-response). Non-response directly affects the effective sample size and can lead to non-response bias. In statistical survey design, the sampling error is heavily influenced by the actual size of the responding sample rather than just the initial planned sample. Furthermore, non-response alters the representativeness of the sample, which directly impacts the accuracy and error calculations of the survey estimates. Therefore, both unit and item non-responses are crucial factors when evaluating sampling and non-sampling errors, rendering Statement II false.

Consequently, both Statement I and Statement II are false.