For variables sampling purposes, changes in certain parameters affect sample size positively while changes in others have a negative effect. In this regard, which statement is true?

For variables sampling purposes, changes in certain parameters affect sample size positively while changes in others have a negative effect. In this regard, which statement is true?

• A. An increase in beta risk reduces sample size.
• B. Population size affects sample size inversely, i.e., as population size increases, sample size decreases.
• C. An increase in alpha risk, increases sample size.
• D. As materiality (M) increases, sample size increases.

Answer: (A)

In variable sampling, the amount of testing you need is driven by how strict you want to be about risks and misstatements. When beta risk is increased, you’re accepting a higher chance of not detecting a misstatement, so you can get away with a smaller sample. Conversely, to reduce beta risk you would need a larger sample because you’re aiming for stronger assurance. The other statements don’t fit because they describe relationships that aren’t correct in this context. Population size doesn’t simply reduce sample size as it grows; the finite population correction matters mainly when you sample a sizable portion of a small population, and otherwise population size has little direct impact. Increasing alpha risk makes it easier to tolerate false positives, which actually allows for a smaller sample, not a larger one. Similarly, increasing materiality means you can tolerate larger misstatements, which reduces the required sample size, not increases it.

In variable sampling, the amount of testing you need is driven by how strict you want to be about risks and misstatements. When beta risk is increased, you’re accepting a higher chance of not detecting a misstatement, so you can get away with a smaller sample. Conversely, to reduce beta risk you would need a larger sample because you’re aiming for stronger assurance.

The other statements don’t fit because they describe relationships that aren’t correct in this context. Population size doesn’t simply reduce sample size as it grows; the finite population correction matters mainly when you sample a sizable portion of a small population, and otherwise population size has little direct impact. Increasing alpha risk makes it easier to tolerate false positives, which actually allows for a smaller sample, not a larger one. Similarly, increasing materiality means you can tolerate larger misstatements, which reduces the required sample size, not increases it.