Question

researchers studied the mean egg length (in millimeters) for a bird population. after taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). what is the value of the margin of error?
choose the correct answer below
a. 15 mm
b. 7.5 mm
c. 1.96
d. 52.5 mm

Explanation:

Step1: Find the sample mean

The sample mean $\bar{x}$ is the mid - point of the confidence interval. The formula for the mid - point of an interval $(a,b)$ is $\bar{x}=\frac{a + b}{2}$.
For the interval $(45,60)$, we have $\bar{x}=\frac{45+60}{2}=\frac{105}{2}=52.5$.

Step2: Calculate the margin of error

The margin of error $E$ is given by $E=\bar{x}-a$ (or $E = b-\bar{x}$).
Using $E=\bar{x}-a$, with $\bar{x}=52.5$ and $a = 45$, we get $E=52.5 - 45=7.5$.

Answer:

B. \(7.5\) mm