Final answer:
The width of a 95 percent confidence interval for the true population proportion with 12 successes in a sample of 25 is most reasonably estimated to be ±.196 from the given options.
Step-by-step explanation:
To calculate the width of a 95 percent confidence interval for the true population proportion with 12 successes in a sample of 25, we will use the confidence interval formula for a population proportion:
p' ± EBP
where p' is the sample proportion and EBP (Error Bound for Proportion) is the margin of error for the confidence interval.
The sample proportion (p') is calculated as the number of successes divided by the total sample size, which is 12/25. The margin of error (EBP) depends on the standard error of the proportion and the z-score associated with the 95% confidence level (which is approximately 1.96).
The standard error (SE) for the population proportion is calculated using the formula:
SE = √{[p'(1 - p')] / n}
Substituting the known values, we have:
SE = √{[(12/25)(1 - 12/25)] / 25}
The margin of error (EBP) is then calculated as:
EBP = Z * SE
EBP = 1.96 * SE
Substituting SE from above, we can solve for EBP to find the width of the confidence interval. After finding EBP, we double it to get the full width (the sum of the positive and negative margins around p').
Without completing these calculations, we cannot be precise, but we can look for a plausible range in the provided options. The value of ±.196 seems to be reasonable for a sample size of 25. The other given options are not within a plausible range for a sample size of 25 in making a reasonable estimation of a population proportion.