Suppose that a city planning commission wants to know the proportion of city residents who support installing streetlights in the downtown area. Two different people independently selected random samples of city residents and used their sample data to construct the following confidence intervals for the population proportion:
Interval 1: (0.28, 0.34) Interval 2: (0.31, 0.33)
a. Explain how it is possible that the two confidence intervals are not centered in the same place.
b. Which of the two intervals conveys more precise information about the value of the population proportion?
c. If both confidence intervals have a 95% confidence level, which confidence interval was based on the smaller sample size? How can you tell?
d. If both confidence intervals were based on the same sample size, which interval has the higher confidence level? How can you tell?