Final answer:
The sample size in a study is influenced by the desired power, which should be adequately high, typically 80% or more, and the level of significance, generally set to 0.05. If the population proportion is known, such as 0.6 or 0.5, it can be used in a formula to calculate the minimum sample size required for a certain confidence level and margin of error.
Step-by-step explanation:
When designing a study, the required sample size is crucial to ensure the study will have sufficient power to detect a desired effect at a given level of significance. The level of significance (alpha) is typically set to 0.05, and in this case, you desire an 80% power (meaning 1-β, where β is the risk of a Type II error, is 0.8). To determine sample size, you need to account for the desired power, the level of significance, the effect size you wish to detect, and the population proportion if known.
For a population proportion with prior knowledge, such as 0.6 or 0.5, you can use a formula derived from the binomial distribution and normal approximation to calculate the minimum sample size required. The formula incorporates the population proportion (P), the desired margin of error (E), the z-score corresponding to the desired confidence level, and the power of the test. For instance, to achieve a 95 percent confidence interval within three percentage points (E=0.03) of the population proportion presumed to be 0.5, the z-score for a 95 percent confidence level is approximately 1.96, and you would use the standard error formula SE = √[P(1-P)/n] to solve for the sample size (n).