Question

Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights,recorded in inches (brother's height minus sister's 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?

Answer 1

The margin of error for the provided 95% confidence interval is 2.55 inches, which is calculated by taking the average of the difference between the upper and lower bounds of the confidence interval.

Step-by-step explanation:

The margin of error for a confidence interval is the distance from the mean of the interval to one of its endpoints. In the provided case with a 95% confidence interval for the mean difference in heights of (-0.76, 4.34), the margin of error can be calculated by finding the difference between the upper bound and the lower bound and then dividing by 2. Formally:

Margin of Error = (Upper Bound - Lower Bound) / 2

Substituting in the given values:

Margin of Error = (4.34 - (-0.76)) / 2

Margin of Error = (4.34 + 0.76) / 2

Margin of Error = 5.10 / 2

Margin of Error = 2.55 inches