Professors of accountancy are in high demand at American universities. A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand. Assume the distribution is normally distributed. Construct a 90% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars.
A) [107.7520, 162.2480]
B) [129.8497, 140.1503]
C) [130.0260, 139.9740]
D) [131.0268, 138.9732]

Question

Quizplus · Accepted Answer

The 90% confidence interval for the mean salary of new accounting professors is calculated using the formula for the confidence interval of the mean with known standard deviation: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level (for 90%, $z = 1.645$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 135$, $\sigma = 16$, $n = 28$), we get the interval $[129.8497, 140.1503]$.

Professors of Accountancy Are in High Demand at American Universities