Question

The results of a survey show that the percent of adults in a certain town who want to add bike lanes to amajor roadway is in the interval (0.57, 0.65) (9 points)(a) What is the point estimate for the percent who want to add the bike lanes?(b) What is the poll's margin of error?(c) If the town's adult population is 31,526, what is the best estimate for the number of people whowould support the bike lanes?

Answer 1

If we know the confidence interval for the proportion, the point estimate will be at the center of this interval.

Then, we can calculate the point estimate p as the average between the boundaries of the interval:

`p=(0.57+0.65)/(2)=(1.22)/(2)=0.61`

The margin of error can be calculated, knowing the interval, as half the difference between the upper boundary and the lower boundary of the interval:

`\text{MOE}=(UB-LB)/(2)=(0.65-0.57)/(2)=(0.08)/(2)=0.04`

The margin of error is 0.04. This margin of error is also the absolute difference between any boundary of the interval and the point estimate.

If the town's population is 31,526, the best estimate for the number of people who

would support the bike lanes is to use the point estimate as the proportion:

`X=p\cdot N=0.61\cdot31526\approx19231`

Answer:

a) The point estimate is p=0.61

b) The margin of error is MOE = 0.04

c) The best estimate is X=19231