Using a previous exercise about Hallux abducto valgus (HAV) (deformation of the big toe that often requires surgery). Doctors used x-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here is the data:
28 32 25 34 38 26 25 18 30 26 28 13 20
21 17 16 21 23 14 32 25 21 22 20 18 26
16 30 30 20 50 25 26 28 31 38 32 21
It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Carry out the Solve and Conclude steps of a 95% confidence interval for the mean HAV angle in the population of all such patients.
A good way to judge the effect of an outlier is to do your analysis twice, once with the outlier and a second time without it. Using the above data follow a Normal distribution quite closely except for one patient with HAV angle 50 degrees, a high outlier.
(a) Find the 95% confidence interval for the population mean based on the 37 patients who remain after you drop the outlier
(b) Compare your interval in (a) with your interval in part 1. What is the most important effect of removing the outlier.
In order to find the 95% confidence interval for this question, we will use the following formula:
confidence interval = mean +/- z(sd/square root n)
Where z for 95% confidence equal is 1.96, sd is the standard deviation and n is the number of samples.
Mean = sum of all data points/n
A complete, step by step solution to solve the 95% confidence interval for a specific data set. Second portion of this answer investigates the effect of removing an outlier from the same data set.