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Chapter 8: 8.44 (page 330)

Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.

Short Answer

Expert verified

If the margin of error is small, population mean is estimated using x炉and precision of estimate is high.

Step by step solution

01

Given Information

Confidence level is 100(1-伪)%

Sample mean is x鈥�

Population mean is 渭

Margin of error isE

02

Explanation

As margin of error is equal to the half of the length of the confidence interval. x-is the midpoint of the confidence interval.

With particular level of confidence 100(1-伪)%, x-is deviated from 渭by Eunits.

The maximum possible error is E(margin of error).

Hence, if the margin of error is small, population mean is estimated using x-results in high precision.

This is how the margin of error determines the precision with which sample mean estimates a population mean.

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Most popular questions from this chapter

Suppose that you take500 simple random samples from a population and that, for each sample, you obtain a 90%confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown parameter?

Political Prisoners. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat. Alienation, and Perceived Permanent Change". According to the article. the mean duration of imprisonment for 32 patients with chronic PTSD was 33.4months. Assuming that 蟽=42months, determine a 95%confidence interval for the mean duration of imprisonment,渭. of all East German political prisoners with chronic PTSD. Interpret your answer in words.

Two t-curves have degrees of freedom 12 and 20 , respectively. Which one more closely resembles the standard normal curve? Explain your answer.

In each Exercises 8.11-8.16, we provide a sample mean, sample size, and population standard deviation. In each case, perform the following Lacks.

a. Find a 95%confidence interval for the population mean. (Note: You may want to review Example 8.2, which begins on the page 316)

b. Identify and interpret the margin of error.

c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.

x^=35,n=25,蟽=4

The value of a statistic used to estimate a parameter is called a ______ of the parameter.
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