Questions: Interpret the confidence interval correctly: Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of ± 3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are confident that the of registered voters planning on voting for Robert Smith is between and -

Interpret the confidence interval correctly:
Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of ± 3%." The margin of error was based on a 95% confidence level.
Fill in the blanks to obtain a correct interpretation of this confidence interval.
We are confident that the of registered voters planning on voting for Robert Smith is between and -

Transcript text: Interpret the confidence interval correctly: Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that " $52 \%$ of registered voters plan on voting for Robert Smith with a margin of error of $\pm 3 \%$." The margin of error was based on a $95 \%$ confidence level. Fill in the blanks to obtain a correct interpretation of this conflidence interval. Wo are $\qquad$ confident that the $\qquad$ of registered voters $\qquad$ planning on voting for Robert Smith is between $\qquad$ and $\qquad$ -

Solution

Solution Steps

Step 1: Given Information

We have a nationwide random sample of registered voters indicating that $ 52\% $ plan on voting for Robert Smith, with a margin of error of $ \pm 3\% $ at a $ 95\% $ confidence level.

Step 2: Calculate the Confidence Interval

To find the confidence interval, we calculate the lower and upper bounds using the sample proportion and the margin of error:

Lower Bound: \[ \text{Lower Bound} = 0.52 - 0.03 = 0.49 \]
Upper Bound: \[ \text{Upper Bound} = 0.52 + 0.03 = 0.55 \]

Step 3: Interpret the Confidence Interval

We interpret the confidence interval as follows: We are $ 95\% $ confident that the proportion of registered voters planning on voting for Robert Smith is between $ 49\% $ and $ 55\% $.