Final answer:
The smallest sample size given, which is 60, will produce the widest 95% confidence interval when the sample proportion is 0.5 because the width of the confidence interval is inversely proportional to the square root of the sample size.
Step-by-step explanation:
The student asked which sample size will produce the widest 95% confidence interval, given a sample proportion of 0.5. To answer this, it's important to understand that the width of a confidence interval for a proportion is affected by the sample size, with larger sample sizes leading to narrower confidence intervals. The width of the confidence interval is inversely proportional to the square root of the sample size (n). Specifically, the formula for the 95% confidence interval for a sample proportion (p) is given by:
p ± z * sqrt(p(1-p)/n)
Where z is the z-score corresponding to the 95% confidence level. As n increases, the term sqrt(p(1-p)/n) decreases, leading to a narrower interval. Among the provided sample sizes (70, 60, 80, 90), the smallest sample size will result in the widest confidence interval.
Therefore, the correct answer is:
B. 60