Construct a 99% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standarddeviation of 3.8 years. Round to the nearest tenth.
A) (19.9, 24.9)
B) (16.3, 26.9)
C) (17.2, 23.6)
D) (18.7, 24.1)

Question

Quizplus · Accepted Answer

The 99% confidence interval for the population mean is calculated using the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 99%, $z \approx 2.576$), $\sigma$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $22.4 \pm 2.576\frac{3.8}{\sqrt{19}}$ gives the interval (19.9, 24.9) when rounded to the nearest tenth.

Construct a 99% Confidence Interval for the Population Mean, μ