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 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. Carry out the Solve and Conclude steps of a 95% confidence interval for the mean HAV angle in the population of all such patients. x bar = s = confidence interval bounds: degree to

Answer 1

From the given data, the following statistics are calculated:

n = Sample size = 38

$\bar{x}$ = Sample mean = 976/38 = 25.6842

s = Sample SD = 8.1177

SE = s/$\sqrt{n}$ = 8.1177/ = 1.3169

V38

$\alpha$ = 0.05

From Table, Critical value of Z = 1.96.

95% Confidence Interval:

$\bar{x}$$\pm$ Z SE

= 25.6842 $\pm$ 1.96 X 1.3169

= 25.6842 $\pm$ 2.5810

=( 23.10, 28.27)

So, the required answers are:

$\bar{x}$ = 25.68

s = 8.118

confidence interval bounds:

23.10 to 28.27