Question

a. Calculate the following example’s Margin of Error and confidence interval (show your work for possibility or partial credit) 200 laboratory sample orders were reviewed and it was determined that the mean turnaround time was 55.6 minutes for reporting the results to the physician. The turnaround times were normally distributed and showed a sample standard deviation of 5.2 minutes. The researcher s would like to construct a 90% confidence interval. Calculate the 90% confidence interval:

b. Explain in statistical terms, what the answer in question 19 is saying about the mean turnaround time of laboratory samples in the broader population.

Answer 1

Sample size = n = 200

Sample mean = = 55.6

Standard deviation = s = 5.2

a) We have to construct 90% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 200 - 1 = 199

Level of significance = 0.10

tc = 1.653   ( Using t table)

So confidence interval is ( 55.6 - 0.6076 , 55.6 + 0.6076) = > ( 54.9924 , 56.2076)

b)

We are 90% confidence that the population mean lies into above interval.