20 Hallux abducto valgus call it HAV is a deformation of th

20. \'\' 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 consecutive 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.

It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. The data follow a Normal distribution quite closely except for one patient with HAV angle 52 degrees, a high outlier. 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.

(a) Find the 95% confidence interval for the population mean based on the 37 patients who remain after you drop the outlier. (Round your answers to two decimal places.)

___________° to_________ °

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=24.7297
Standard deviation( sd )=6.63597
Sample Size(n)=37
Confidence Interval = [ 24.7297 ± t a/2 ( 6.63597/ Sqrt ( 37) ) ]
= [ 24.7297 - 2.028 * (1.09) , 24.7297 + 2.028 * (1.09) ]
= [ 22.52,26.94 ]