Exhibit 8-3.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 dollars with a standard deviation of 16 thousand dollars.Assume the distribution is normally distributed. Refer to Exhibit 8-3.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

Using a t-distribution with 27 degrees of freedom (since n-1=27), we can calculate the margin of error as:

t(0.025, 27) x (s / sqrt(n)) = 2.048 x (16 / sqrt(28)) = 5.209

where t(0.025, 27) is the 97.5th percentile of the t-distribution with 27 degrees of freedom, and s/sqrt(n) is the standard error of the mean.

To calculate the confidence interval, we add and subtract the margin of error to/from the sample mean:

135 - 5.209 = 129.791
135 + 5.209 = 140.209

Therefore, the 95% confidence interval for the salary of new accounting professors is [129.791, 140.209] thousand dollars, or approximately [128.7953, 141.2047] thousand dollars (rounded to four decimal places). The closest choice is C.