Express the confidence interval 121.7 << 289.5 in the form of + ME. T + ME +
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 2GP
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![**Expressing Confidence Intervals**
To express a given confidence interval in the form \(\bar{x} \pm ME\), where \(\mu\) is the population mean, follow these steps:
Given the confidence interval: \(121.7 < \mu < 289.5\)
1. Calculate the sample mean \(\bar{x}\):
\[
\bar{x} = \frac{121.7 + 289.5}{2} = 205.6
\]
2. Calculate the margin of error (ME):
\[
ME = 289.5 - 205.6 = 83.9
\]
So, the confidence interval \(\bar{x} \pm ME\) can be written as:
\[
\bar{x} \pm ME = 205.6 \pm 83.9
\]
Fill in the boxes as follows:
\[
\boxed{205.6} \pm \boxed{83.9}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51fab9e4-c55b-4f18-999a-c6ac10434c60%2F3e07c31d-797e-4891-858c-4e66ea3d3198%2Frskyozp_processed.png&w=3840&q=75)
Transcribed Image Text:**Expressing Confidence Intervals**
To express a given confidence interval in the form \(\bar{x} \pm ME\), where \(\mu\) is the population mean, follow these steps:
Given the confidence interval: \(121.7 < \mu < 289.5\)
1. Calculate the sample mean \(\bar{x}\):
\[
\bar{x} = \frac{121.7 + 289.5}{2} = 205.6
\]
2. Calculate the margin of error (ME):
\[
ME = 289.5 - 205.6 = 83.9
\]
So, the confidence interval \(\bar{x} \pm ME\) can be written as:
\[
\bar{x} \pm ME = 205.6 \pm 83.9
\]
Fill in the boxes as follows:
\[
\boxed{205.6} \pm \boxed{83.9}
\]
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