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4.5.3 Qutz: Margin of Eror and Confidence Intervals
Question 9 of 10
An confidence interval for a proportion is found to be . What
is the sample proportion?
A. 0.56
B. 0.54
C. 0.55
D. 0.58

Ask by Gough Guerrero. in the United States
Jan 30,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The sample proportion is 0.55.

Solution

To determine the sample proportion from the given confidence interval , we can use the following approach:
A confidence interval for a proportion is typically expressed as:
This means that the center of the interval represents the sample proportion. To find the sample proportion, calculate the midpoint of the interval:
Therefore, the correct answer is:
C. 0.55

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Beyond the Answer

To find the sample proportion from a confidence interval, you can calculate the midpoint of the interval. For the interval , the sample proportion is:
So, the answer is C. 0.55.
The margin of error can be calculated as half the width of the interval. In this case, the width is , and half of that (the margin of error) is . This means the sample proportion is actually with a margin of error of , leading to the confidence interval you’ve been given!

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