twenty - four pairs of adult brothers and sisters were sampled at random from a population. the difference…

twenty - four pairs of adult brothers and sisters were sampled at random from a population. the difference in heights, recorded in inches (brothers height minus sisters height), was calculated for each pair. the 95% confidence interval for the mean difference in heights for all brother - and - sister pairs in this population was (-0.76, 4.34). what is the margin of error for the confidence interval?\n\n$\frac{4.34 - 0.76}{2}=1.79$\n\n$\frac{4.34-(-0.76)}{2}=2.55$\n\n$4.34 - 0.76 = 3.58$\n\n$4.34-(-0.76)=5.10$

twenty - four pairs of adult brothers and sisters were sampled at random from a population. the difference in heights, recorded in inches (brothers height minus sisters height), was calculated for each pair. the 95% confidence interval for the mean difference in heights for all brother - and - sister pairs in this population was (-0.76, 4.34). what is the margin of error for the confidence interval?\n\n$\frac{4.34 - 0.76}{2}=1.79$\n\n$\frac{4.34-(-0.76)}{2}=2.55$\n\n$4.34 - 0.76 = 3.58$\n\n$4.34-(-0.76)=5.10$

Answer

Explanation:

Step1: Recall margin - of - error formula

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

Step2: Identify $a$ and $b$ values

Here, $a=-0.76$ and $b = 4.34$.

Step3: Calculate the margin of error

$E=\frac{4.34-(-0.76)}{2}=\frac{4.34 + 0.76}{2}=\frac{5.1}{2}=2.55$

Answer:

$\frac{4.34-(-0.76)}{2}=2.55$ (Second option)