The employees of Cybertronics Inc.need to complete a certification online.A random sample of 16 employees gives an average time for completion of all the coursework and passing the tests of 20 hours.The population standard deviation is unknown but the sample standard deviation is 6 hours.You can assume that the population of employees is fairly large.Construct a 95% confidence interval for the average time required to complete the certification.
A) 17.06 to 22.94
B) 17.37 to 22.63
C) 17.68 to 22.32
D) 17.99 to 22.01
E) 18.31 to 21.69

Question

Quizplus · Accepted Answer

Since the population standard deviation is unknown, we use the t-distribution with degrees of freedom n-1 = 15 and a confidence level of 95%. From the t-distribution table, the t-value for this case is 2.131.

The margin of error is calculated as:
ME = t*(s/sqrt(n)) = 2.131*(6/sqrt(16)) = 3.197

The confidence interval is then:
sample mean ± margin of error = 20 ± 3.197 = (16.803, 23.197)

Therefore, the best choice is B.

The Employees of Cybertronics Inc