Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. The 95% confidence interval is
A) 12.45 to 17.85 hours.
B) 14.62 to 15.78 hours.
C) 13.88 to 14.29 hours.
D) 10.65 to 20.22 hours.
E) 11.98 to 18.02 hours.

Question

Quizplus · Accepted Answer

To find the 95% confidence interval, we use the formula:
CI = x̄ ± zα/2 * (σ/√n)
where x̄ is the sample mean, σ is the population standard deviation (which we don't know, so we use the sample standard deviation), n is the sample size, and zα/2 is the z-score that corresponds to the desired confidence level (0.95) and accounts for the sample size.

Substituting the given values, we get:
CI = 15.2 ± 1.96 * (1.8/√40)
CI = 15.2 ± 0.53
CI = (14.67, 15.73)

Therefore, the best choice is B, which corresponds to the interval (14.62, 15.78) hours, which contains the true population mean with 95% probability.

Suppose 40 Professional Employees Are Randomly Selected