Final answer:
The 95% margin of error in estimating a binomial proportion can be calculated using the formula Margin of Error = Z × sqrt[(pʼqʼ)/n], where Z is the z-score for the desired confidence level, p is the proportion of interest, q is the complement of p, and n is the sample size. Plugging in the given values of p = q = 0.5 and n = 100, we can compute the margin of error as approximately 0.0980.
Step-by-step explanation:
To calculate the 95% margin of error in estimating a binomial proportion p using samples of size n = 100, we can use the formula Margin of Error = Z × sqrt[(pʼqʼ)/n]. In this case, given that p = q = 0.5 and n = 100, we can substitute these values into the formula. Z refers to the z-score corresponding to the desired confidence level; for 95% confidence, Z is approximately 1.96. Plugging in the values, we get Margin of Error = 1.96 × sqrt[(0.5×0.5)/100]. Solving this equation gives us the margin of error as approximately 0.0980 when rounded to four decimal places.