Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the development of a recreational park on the west side of town. A community action group interested in preserving the environment claims that 45% of the town's residents favor the development of a recreational park.

To determine whether the sample supports the population proportion, a simulation of 100 trials is run, each with a sample of 200, using the point estimate of the population. The minimum sample proportion from the simulation is 0.46 and the maximum sample proportion is 0.76.

(a) What is the point estimate of the population?

(b) The margin of error of the population proportion is found using an estimate of the standard deviation. What is the interval estimate of the true population proportion?

(c) The margin of error of the population proportion is found using the half the range.

(d) What is the interval estimate of the true population proportion?4

(e) Is the community action group's claim likely based on either interval estimate of the true population proportion? Explain.

Answer:

a). Point estimate of the population is 0.61.

b). Margin of error = 0.07

Interval estimate of the true population is ± 7%.

c).  Margin of error   = 0.15

d)  Interval estimate of the true population is ± 15%

e). Yes, the community action claim is based on the Interval estimate of the true population calculated from half the range. This is because 62% ± 15% = 47% or 77% where 47% is close to 45% as claimed by the community action group.

Details and calculations.

Given;

Lower bound = 0.46

Upper bound = 0.76

n = 200 (population size)

Solution:

(a)   The point estimate of the population is given as, P = (lower bound + upper bound)/2  

P = (0.46+0.76)/2

P = 0.61

Point estimate of the population is 0.61.

(b)  Margin of error by using the estimate of standard deviation is calculated as follows;

 = Z*√(P*(1-P)/n))

Where Z is assumed to be 1.96 the critical value at 95% confidence interval

1.96*√((0.61*(1-0.61)/200) = 0.06762

                                                  0.07

Margin of error = 0.07

Interval estimate of the true population is ± 7%.

(c)   Using the half of the rage, the margin of error = (upper bound-lower bound)/2

                                                                                  = (0.76-0.46)/2

                                                                                  = 0.15

(d)  Interval estimate of the true population is ± 15%

(e)  Yes, the community action claim is based on the Interval estimate of the true population calculated from half the range. This is because 62% ± 15% = 47% or 77% where 47% is close to 45% as claimed by the community action group.