A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence,what is the confidence interval for the population mean?
A)5.04 and 5.96
B)5.06 and 5.94
C)2.67 and 8.33
D)4.40 and 6.60

Question

Quizplus · Accepted Answer

The confidence interval for the population mean can be calculated using the formula: $\bar{x} \pm z\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $z$ is the z-score corresponding to the confidence level. For a 99% confidence level, the z-score is approximately 2.58. Plugging in the given values: $5.5 \pm 2.58\frac{1.1}{\sqrt{42}}$, we get the interval $5.04$ to $5.96$.

A Random Sample of 42 College Graduates Revealed That They