The employees of Cybertronics Inc.need to complete a certification online.A random sample of 49 employees gives an average time for completion of all the coursework and passing the tests of 6 hours.Assume that the population standard deviation is 6 hours and the population of employees is fairly large.Construct a 95% confidence interval for the average time required to complete the certification.
A) 18.28 to 21.72
B) 18.32 to 21.68
C) 18.36 to 21.64
D) 18.40 to 21.60
E) 19.76 to 20.24

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a population mean with a known population standard deviation:

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 critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case).

Plugging in the given values, we have:

CI = 6 ± 1.96*(6/√49)
CI ≈ 6 ± 1.96*(0.857)
CI ≈ 6 ± 1.68
CI ≈ (4.32, 7.68)

Therefore, the 95% confidence interval for the average time required to complete the certification is approximately 4.32 to 7.68 hours. The closest answer choice to this interval is B: 18.32 to 21.68, which is clearly incorrect. None of the answer choices match the interval we found, so the best choice is B, even though it is not a valid answer.

The Employees of Cybertronics Inc