Question

What is the probability that a sample proportion will be within ±0.06 of the population proportion for each of the following sample sizes (rounded to 4 decimal places?

For n = 100, what is the probability?

Answer 1

The question involves calculating the probability that a sample proportion is within a certain range of the population proportion for a sample size of 100, which is based on the concept of confidence intervals in inferential statistics.

Step-by-step explanation:

The student is asking about the probability of a sample proportion being within a certain range of the population proportion for a given sample size, in this case, n = 100. This question pertains to inferential statistics, specifically the concept of confidence intervals for population proportions.

When a student wants to know the probability that a sample proportion will be within ±0.06 of the population proportion for a sample size of 100, they are referring to the confidence level that is related to the sampling distribution's standard error and z-scores associated with that confidence level.

Using the given population proportion (p = 0.5 for symmetry and maximum variability), the formula to calculate the standard error is
`√(p(1-p)/n)`. The z-score for a given confidence level can be obtained from z-tables or statistical software. With these values, the student can calculate the range for the confidence interval and hence the probability.