Question 51

Approximate value of p is needed to determine sample size.

To estimate the proportion, the researcher needs to know the approximate value of p, which represents the expected proportion of the population. This value is crucial in calculating the required sample size for achieving a desired level of precision in the estimate.

A) Standard error

While the standard error is important in assessing the variability of the sample proportion, it is not sufficient on its own to determine the sample size. The standard error is derived from the sample size and the estimated proportion, making it dependent on knowing the value of p.

B) Approximate value of p

This option is essential for determining the sample size because it provides the necessary estimate of the population proportion. Knowing the approximate value of p allows the researcher to calculate the required sample size to achieve a specified margin of error and confidence level.

C) t-value

The t-value is relevant when making inferences about population means, particularly with smaller sample sizes. However, it does not directly assist in determining the sample size needed for estimating a population proportion, thus making it less applicable in this context.

D) Population size

While population size can influence the sample size calculations in finite populations, it is not the primary quantity needed to estimate the proportion. The approximate value of p is more critical for determining the sample size required for accurate estimation.

Conclusion

The approximate value of p is the key factor in determining the sample size needed for estimating a population proportion, as it directly influences the calculations for precision and confidence. All other options either provide supportive information or are relevant in different contexts but do not replace the necessity of knowing p. Thus, option B stands out as the definitive answer.