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 95% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars.
A) [102.1680, 167.832]
B) [127.8247, 142.1753]
C) [128.7958, 141.2042]
D) [129.0735, 140.9265]

Question

Quizplus · Accepted Answer

To construct the confidence interval, we use the formula:
CI = x̄ ± z*(σ/√n)
where x̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z* is the z-score that corresponds to the desired level of confidence (in this case, 95%). Since the sample size is large (n = 28), we can use the z-distribution instead of the t-distribution.
Plugging in the given values, we get:
CI = 135 ± 1.96*(16/√28)
CI = [128.7958, 141.2042] (rounded to four decimal places)
Therefore, the best choice is C.

Professors of Accountancy Are in High Demand at American Universities