construct 90, 95, and 99 perce
construct 90, 95, and 99 percent confidence intervals for thepopulation mean, and state the practical and probabilisticinterpretations of each. Indicate which interpretation you thinkwould be more appropriate to use. Explain why the three intervalsthat you construct are not of equal width. Indicate which of thethree intervals you would prefer to use as an estimate of thepopulation mean, and state the reason for your choice.
In a length of hospitalization study conducted by severalcooperating hospitals, a random sample of 64 peptic ulcer patientswas drawn from a list of all peptic ulcer patients ever admitted tothe participating hospitals and the length of hospitalization peradmission was determined for each. The mean length ofhospitalization was found to be 8.25 days. The population standarddeviation is known to be 3 days.
Answer:
Given that mean = 8.25, population standard deviation = 3 andsample size n = 64
Calculation for 90% confidenceinterval…….{z score for 90% confidence interval is1.64, using z distribution table}
{interval length is difference between lower and upper limits}
There is 0.90 probability that the population mean will liebetween the calculated range
We can be 90% confident that the population mean will liebetween the calculated range
Calculation for 95% confidenceinterval…….{z score for 95% confidence interval is1.96, using z distribution table}
{interval length is difference between lower and upper limits}
There is 0.95 probability that the population mean will liebetween the calculated range
We can be 95% confident that the population mean will liebetween the calculated range
Calculation for 99% confidenceinterval…….{z score for 99% confidence interval is2.58, using z distribution table}
{interval length is difference between lower and upper limits}
There is 0.99 probability that the population mean will liebetween the calculated range
We can be 99% confident that the population mean will liebetween the calculated range
I think practical interpretation is more appropriate to use ascompared to probabilistic interpretation.
Three intervals are not of equal width because the margin oferror is different for each confidence level due to the change inthe critical value. I will prefer 95% confidence interval becauseit is neither narrow like 90% confidence level nor wide like 99%confidence interval.
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
