Question

A recent poll taken by the movie theatre industry shows that 28% of the population attends a movie in a theater at least once a month. A sample of 300 people shows that only 12% of people attends a movie in a theater at least once a month. To determine whether this sample supports the population proportion of 0.28, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.12. The minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28. What is the margin of error of the population proportion using half the range?

Answer 1

+ and -0.09I just took the test

Answer 2

The margin of error for this population proportion using half the range = ±0.09

Explanation:

Confidence Interval is basically an interval of range of values where the true proportion can be found with a certain level of confidence.

Margin of Error is the width of the confidence interval about the central proportion.

For this question, the minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28, hence, the confidence interval for the question is (0.10, 0.28).

The width of this confidence interval = (Upper limit of the interval) - (Lower limit of the interval) = 0.28 - 0.10 = 0.18.

Hence, the margin of error for this population proportion using half the range, is 0.18/2 = 0.09.

Written appropriately as ±0.09.

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