a political candidate feels that she performed particularly well in the most recent debate against her…

a political candidate feels that she performed particularly well in the most recent debate against her opponent. her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. the 95% confidence interval for the true difference (post - debate minus pre - debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). what is the margin of error for this confidence interval?\n\n$\frac{0.064+( - 0.014)}{2}=0.025$\n\n$\frac{0.064-( - 0.014)}{2}=0.039$\n\n$0.064+( - 0.014)=0.050$\n\n$0.064-( - 0.014)=0.078$

a political candidate feels that she performed particularly well in the most recent debate against her opponent. her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. the 95% confidence interval for the true difference (post - debate minus pre - debate) in proportions of likely voters who would vote for this candidate was (-0.014, 0.064). what is the margin of error for this confidence interval?\n\n$\frac{0.064+( - 0.014)}{2}=0.025$\n\n$\frac{0.064-( - 0.014)}{2}=0.039$\n\n$0.064+( - 0.014)=0.050$\n\n$0.064-( - 0.014)=0.078$

Answer

Explanation:

Step1: Recall margin - of - error formula

The margin of error $E$ for a confidence interval $(a,b)$ is given by $E=\frac{b - a}{2}$.

Step2: Identify $a$ and $b$ values

Here, $a=-0.014$ and $b = 0.064$.

Step3: Calculate margin of error

$E=\frac{0.064-(-0.014)}{2}=\frac{0.064 + 0.014}{2}=\frac{0.078}{2}=0.039$.

Answer:

$\frac{0.064-(-0.014)}{2}=0.039$ (Second option)