Based on a poll of 100 citizens, a community action group claims that 38% of the population is in favor of the construction of a senior center using tax dollars. A business group claims that the poll is not valid and that 65% of the citizens favor the construction of the senior center using tax dollars.

To determine whether this sample supports the population proportion of 0.38, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.65. The minimum sample proportion from the simulation is 0.42, and the maximum sample proportion from the simulation is 0.72.

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?

The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).

What is a standard deviation?

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

B.) Because the margin of error is ±2σ, therefore, we can write,

Margin Of Error = (±0.05)×2 = ±0.10

C.) The interval can be estimated as,

Interval = 0.65±0.10

= 0.65-0.10, 0.65+0.10

= 0.55, 0.75

Hence, the interval estimate of the true population proportion is (0.55, 0.75).

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