Question: Hallux abducto valgus (call it HAV)is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here are 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 26 28 31 38 38 21
It is reasonable to regard these patients as a random sample of young patients who require HAV surgery.
(a) Construct a 95% confidence interval for the mean HAV angle in the population of all such patients.
(b) Construct a histogram and assess the shape, center, and spread. Remove the patient(s) that who are outliers.
(c) Construct a 95% confidence interval for the population mean based on the remaining patients after you drop the outlier(s).
(d) Compare your interval in (a) with your interval in (c). What is the most important effect of removing the outlier(s)?