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Chapter 8: Problem 7

Briefly explain the difference between a confidence level and a confidence interval.

Short Answer

Expert verified
A confidence level refers to the degree of certainty, expressed as a percentage, that a certain statistical estimate is reliable. A confidence interval, however, represents the range within which the true population parameter is likely to fall with that certain degree of confidence. While the confidence level measures the certainty about the sample data, the confidence interval provides an estimate of the variability around a population parameter.

Step by step solution

01

Defining Confidence Level

A Confidence level, in statistical analysis, reflects the degree of certainty that a given parameter lies within a certain interval. It is expressed as a percentage, with commonly used confidence levels being 90%, 95%, or 99%. A 95% confidence level signifies that if the same sample were drawn 100 times, then approximately 95 times out of those 100, the confidence interval would contain the population parameter.
02

Defining Confidence Interval

A Confidence interval, on the other hand, represents the range within which the true population parameter lies with a certain degree of confidence. It is expressed as an interval from a lower limit to an upper limit. The confidence interval gives an estimate of the variability around the mean and is determined using data from a sample.
03

Comparison between Confidence Level and Confidence Interval

While they are related, the confidence level and confidence interval are not the same. The confidence level is a measure of certainty about the data while the confidence interval provides an estimated range of values within which the true value of the population parameter is likely to fall.

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Most popular questions from this chapter

What is the point estimator of the population mean, \(\mu\) ? How would you calculate the margin of error for an estimate of \(\mu\) ?

When one is attempting to determine the required sample size for estimating a population mean, and the information on the population standard deviation is not available, it may be feasible to take a small preliminary sample and use the sample standard deviation to estimate the required sample size, \(n .\) Suppose that we want to estimate \(\mu\), the mean commuting distance for students at a community college, to a margin of error within 1 mile with a confidence level of \(95 \%\). A random sample of 20 students yields a standard deviation of \(4.1\) miles. Use this value of the sample standard deviation, \(s\), to estimate the required sample size, \(n .\) Assume that the corresponding population has an approximate normal distribution.

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave a mean water usage of \(3415.70\) gallons over a 1-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is \(389.60\) gallons. Make a \(95 \%\) confidence interval for the average monthly residential water usage for all households in this city.

According to the 2015 Physician Compensation Report by Medscape (a subsidiary of WebMD), American orthopedists earned an average of \(\$ 421,000\) in 2014 . Suppose that this mean is based on a random sample of 200 American orthopaedists, and the standard deviation for this sample is \(\$ 90,000\). Make a \(90 \%\) confidence interval for the population mean \(\mu\).

Determine the sample size for the estimate of \(\mu\) for the following. a. \(E=.17, \quad \sigma=.90\), confidence level \(=99 \%\) b. \(E=1.45, \quad \sigma=5.82, \quad\) confidence level \(=95 \%\) c. \(E=5.65, \quad \sigma=18.20, \quad\) confidence level \(=90 \%\)
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