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) [128.7953,141.2047]
D) [129.0735,140.9265]

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean salary of new accounting professors, we will use the formula:
CI = X̄ ± Z*(σ/√n)
where X̄ is the sample mean ($135), σ is the population standard deviation ($16), n is the sample size (28), and Z* is the critical value from the standard normal distribution corresponding to a 95% confidence level (1.96).
Plugging in the values, we get:
CI = 135 ± 1.96*(16/√28)
CI = [128.7953, 141.2047]
Therefore, the best choice is C.

Professors of Accountancy Are in High Demand at American Universities