Construct a 95% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A sample of 20 part-time workers had mean annual earnings of $3120 with a standard deviationof $677. Round to the nearest dollar.
A) ($2803, $3437)
B) ($1324, $1567)
C) ($2135, $2567)
D) ($2657, $2891)

Question

Quizplus · Accepted Answer

The 95% 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 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Substituting the given values: $3120 \pm 1.96\frac{677}{\sqrt{20}}$, we get the interval ($2803, $3437) when rounded to the nearest dollar.

Construct a 95% Confidence Interval for the Population Mean, μ