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Chapter 8: Problem 1

Explain what is meant by "margin of error" in point estimation.

Short Answer

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Short Answer: Margin of error is a measure of uncertainty around a point estimate, which is a single value approximation of an unknown population parameter derived from sampled data. The margin of error indicates how much the point estimate can deviate from the true population value and is used with a confidence level to construct a confidence interval for the population parameter. By considering the margin of error, researchers can accurately communicate and interpret statistical results, acknowledging the potential variability in their point estimates.

Step by step solution

01

Define Point Estimation

Point estimation is a statistical method to approximate the value of an unknown population parameter using a single value called the point estimate, derived from the sampled data. This can be the mean, median, or mode of a sample of the population depending on the context.
02

Introduce Margin of Error

Margin of error is a measure of the uncertainty around a point estimate. It is a range within which the true population parameter is believed to lie with a certain level of confidence. In other words, it indicates how much the point estimate can be "off" from the true population value.
03

Describe Confidence level and Confidence Interval

The confidence level is the probability that the true population parameter lies within the margin of error. It is typically expressed as a percentage, such as 95% or 99%. The confidence interval is a range that contains the point estimate and is calculated by adding and subtracting the margin of error from the point estimate.
04

Explain how to calculate Margin of Error

The margin of error can be calculated by multiplying the standard error of the point estimate with a critical value that reflects the desired confidence level. The standard error measures the variability of the point estimate, and the critical value depends on the chosen confidence level and the underlying distribution of the data (e.g., a z-score for a normal distribution or a t-score for a t-distribution).
05

Summarize the relationship between Margin of Error and Point Estimation

In summary, margin of error is a measure of uncertainty around a point estimate. It indicates how much the point estimate can deviate from the true population value, and it is used in conjunction with the confidence level to provide a confidence interval for the population parameter. By considering the margin of error, researchers and practitioners can communicate and interpret statistical results with more accuracy and understand the potential variability in their point estimates.

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Most popular questions from this chapter

A random sample of \(n=900\) observations from a binomial population produced \(x=655\) successes. Estimate the binomial proportion \(p\) and calculate the margin of error.

A random sample of \(n\) measurements is selected from a population with unknown mean \(\mu\) and known standard deviation \(\sigma=10 .\) Calculate the width of a \(95 \%\) confidence interval for \(\mu\) for these values of \(n\) : a. \(n=100\) b. \(n=200\) c. \(n=400\)

An experimental rehabilitation technique was used on released convicts. It was shown that 79 of 121 men subjected to the technique pursued useful and crime- free lives for a three-year period following prison release. Find a \(95 \%\) confidence interval for \(p\), the probability that a convict subjected to the rehabilitation technique will follow a crime-free existence for at least three years after prison release.

A random sampling of a company's monthly operating expenses for \(n=36\) months produced a sample mean of \(\$ 5474\) and a standard deviation of \(\$ 764\). Find a \(90 \%\) upper confidence bound for the company's mean monthly expenses.

Refer to Exercise 8.5 . What effect does an increased sample size have on the margin of error?
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