Questions: A confidence interval was constructed to approximate a population proportion. The interval was from 27.5% to 35.5%. The sample proportion that was used to construct this interval was 30.5%. True False

A confidence interval was constructed to approximate a population proportion. The interval was from 27.5% to 35.5%. The sample proportion that was used to construct this interval was 30.5%. True False

Transcript text: A confidence interval was constructed to approximate a population proportion. The interval was from $27.5 \%$ to $35.5 \%$. The sample proportion that was used to construct this interval was $30.5 \%$. True False

Solution

Solution Steps

To determine if the statement is true or false, we need to check if the sample proportion lies within the given confidence interval. The confidence interval is from 27.5% to 35.5%, and the sample proportion is 30.5%. If 30.5% is within the interval, the statement is true; otherwise, it is false.

Step 1: Define the Confidence Interval and Sample Proportion

The confidence interval is given as $27.5\%$ to $35.5\%$. The sample proportion is $30.5\%$.

Step 2: Check if the Sample Proportion Lies Within the Confidence Interval

We need to verify if the sample proportion $30.5\%$ is within the interval $[27.5\%, 35.5\%]$.

Step 3: Evaluate the Condition

The condition to check is: \[ 27.5\% \leq 30.5\% \leq 35.5\% \]