Question

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? (0.55,0.75) (0.28,0.48) (0.45,0.85) (0.18,0.58)

Answer 1

(0.55, 0.75)

Explanation:

The standard deviation and range are both used to measure the spread of a data set. The number of the range and standard deviation gives us information in its own way how spaced out the data are due to the fact that they are both a measure of variation. However, there is not an explicit relationship between the range and standard deviation, there is a rule of thumb that can be useful to relate these two statistics. This relationship is sometimes referred to as the range rule for standard deviation.

The range is estimated to be 6 standard deviations wide. Therefore, the standard deviation is:

Standard deviation= maximum sample proportion - minimum sample proportion / 6

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is defined as a statistic showing the amount of random sampling error in the result of a survey. The greater the margin of error, the lesser the confidence that a poll result would reflect the result of a survey of the entire population.

Here, the margin of error is ±2σ, so:

ME = ±0.10

Interval estimation in statistics is the use of sample data to compute an interval of possible values of an unknown population parameter. This is therefore in contrast to point estimation, which gives a single value.

Therefore, the interval estimate is:

(0.65 - 0.10, 0.65 + 0.10)

(0.55, 0.75)