A researcher has conducted a survey using a simple random sample of 500 golf club members to create a confidence interval to estimate the proportion of golf club members favoring a 1% annual increase in dues to remodel the clubhouse. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 125 people instead of 500 golf club members. Which of the following statements BEST describes how the confidence interval is affected by this change? (3 points)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 fourth the width of the original interval. e. The width of the new interval is about four times the width of the original interval.