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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¯and precision of estimate is high.

Step by step solution

01

Given Information

Confidence level is 100(1-α)%

Sample mean is x—

Population mean is μ

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-α)%, x-is deviated from μby 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

Smelling Out the Enemy. Snakes deposit chemical trails as they travel through their habitats. These trails are often detected and recognized by lizards, which are potential prey. The ability to recognize their predators via tongue flicks can often mean life or death for lizards. Scientists from the University of Antwerp were interested in quantifying the responses of juveniles of the common lizard to natural predator cues to determine whether the behavior is learned or congenital. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Their responses, in number of tongue flicks per twenty minutes, are presented in the following

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a. Determine and interpret a 95%upper confidence bound for the mean calcium intake of all people with incomes below the poverty level.

b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.70

Find the confidence level and ∝ for

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Must the variable under consideration be normally distributed for you to use the z-interval procedure or t-interval procedure? Explain your answer.
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