THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ.
-Calculate the width of the 95% confidence interval estimate.
A)16.12
B)11.38
C)17.86
D)13.58

Question

Quizplus · Accepted Answer

The formula for the confidence interval is:
CI = X̄ ± Z*(σ/√n)
where X̄ is the sample mean, Z is the z-score from the standard normal distribution corresponding to the desired confidence level (here 95%, which gives a z-score of 1.96), σ is the population standard deviation, and n is the sample size.

Plugging in the given values, we have:
CI = 90 ± 1.96*(30/√75)
CI = 90 ± 6.79

The width of the confidence interval is the difference between the upper and lower bounds:
Width = (90 + 6.79) - (90 - 6.79)
Width = 13.58

Therefore, the answer is D: 13.58.