A researcher has conducted a survey using a simple random sample of 225 elementary teachers to create a confidence interval to estimate the proportion of elementary teachers favoring the addition of a soda machine to the cafeteria. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 25 teachers instead of 225 elementary teachers. Which of the following statements best describes how the confidence interval is affected by this change? A: The width of the new interval is about the same width as the original interval.
B: The width of the new interval is about twice the width of the original interval.
C: The width of the new interval is about one-half the width of the original interval.
D: The width of the new interval is about one-third the width of the original interval.
E: The width of the new interval is about three times the width of the original interval.