Math Problem Statement

What is the margin of error for the confidence interval [ 14.70 , 19.20]?

A) 4.0       B) 2.25         C) 5.5         D) 3.65

Solution

The margin of error (ME) for a confidence interval is calculated as half the width of the interval. The confidence interval given is [14.70,19.20][14.70, 19.20].

To find the margin of error, use the formula:

Margin of Error=Upper BoundLower Bound2\text{Margin of Error} = \frac{\text{Upper Bound} - \text{Lower Bound}}{2}

Substitute the given values:

Margin of Error=19.2014.702=4.502=2.25\text{Margin of Error} = \frac{19.20 - 14.70}{2} = \frac{4.50}{2} = 2.25

So, the margin of error is 2.25.

Thus, the correct answer is B) 2.25.


Would you like further explanation or have any questions?

Related questions:

  1. How do you calculate a confidence interval for a sample mean?
  2. What is the relationship between the margin of error and the sample size?
  3. How does the confidence level affect the margin of error?
  4. Can you calculate the margin of error for a confidence interval when only the sample mean and standard deviation are given?
  5. What is the effect of increasing the sample size on the margin of error?

Tip:

When calculating the margin of error, always check the interval bounds carefully to ensure the subtraction is accurate.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Margin of Error

Formulas

Margin of Error = (Upper Bound - Lower Bound) / 2

Theorems

Margin of Error calculation for confidence intervals

Suitable Grade Level

Grades 9-11