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 sample mean?
choose the correct answer below
a. 15.0 mm
b. 52.5 mm
c. 7.5 mm
d. somewhere between 45mm and 60mm, but the exact value cannot be determined without more information.

Explanation:

Step1: Recall the formula for the confidence interval

The confidence interval for the population mean is given by $\bar{x}-E <\mu<\bar{x} + E$, where $\bar{x}$ is the sample mean and $E$ is the margin of error. The mid - point of the confidence interval $(\text{lower limit},\text{upper limit})$ is the sample mean. The formula for the mid - point (sample mean) is $\bar{x}=\frac{\text{lower limit}+\text{upper limit}}{2}$.

Step2: Calculate the sample mean

Given the confidence interval $(45,60)$, where the lower limit $L = 45$ and the upper limit $U=60$. Substitute into the formula $\bar{x}=\frac{45 + 60}{2}$.

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Answer:

B. \(52.5\) mm