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Chapter 3: Problem 45

SKILL BUILDER 2 In Exercises 3.45 to 3.48 , construct an interval giving a range of plausible values for the given parameter using the given sample statistic and margin of error. For \(\mu,\) using \(\bar{x}=25\) with margin of error 3 .

Short Answer

Expert verified
The range of plausible values for the parameter \( \mu \) is [22, 28].

Step by step solution

01

Understand Confidence Interval

A confidence interval is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter (such as \( \mu \)). The interval has an associated confidence level that quantifies the level of confidence that the parameter lies in the interval.
02

Identify the Given Values

The given values are the sample mean, denoted as \( \bar{x} \), which equals to 25 and the margin of error, which is 3.
03

Construct the Confidence Interval

To construct the confidence interval, add and subtract the margin of error from the given sample statistic. Thus, the lower limit of the interval is \( \bar{x} - \) margin of error, which evaluates to \( 25 - 3 = 22 \). The upper limit of the interval is \( \bar{x} + \) margin of error, which evaluates to \( 25 + 3 = 28 \). Therefore, the confidence interval is [22, 28].

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Most popular questions from this chapter

Exercises 3.112 to 3.115 give information about the proportion of a sample that agree with a certain statement. Use StatKey or other technology to find a confidence interval at the given confidence level for the proportion of the population to agree, using percentiles from a bootstrap distribution. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. Find a \(90 \%\) confidence interval if 112 agree and 288 disagree in a random sample of 400 people.

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