Hallux abducto valgus (call it HAV) is a deformation of the big toe that often r
ID: 3517905 • Letter: H
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. 26 34 27 34 38 26 23 19 31 28 28 13 22 21 17 17 20 25 12 34 25 21 22 18 17 28 14 28 30 18 49 26 25 26 32 40 33 22 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. (Round your answer for x to two decimal places and your answer for s to three decimal places. Round your confidence interval bounds to two decimal places.) confidence interval bounds: o to Conclusion O The mean HAV angle among such patients is outside this interval 95% of the time. o we are 95% confidence that the mean HAV angle among such patients is within this interval. O The mean HAV angle among such patients is within this interval 95% of the time. we are 95% confidence that the mean HAV angle among such patients is outside this interval.Explanation / Answer
1) Mean of this interval= sum of all numbers/ total numbers
=sum/n
=963/38
=25.5
S or median= middle number
But in this case as the total number is even so we will calculate as follows:
S= middle two numbers/2
=(25+26)/2
=25.5
2). Confidence interval
= (Confidence level*standard deviation)/square root of n
So confidence level is 95%
We will calculate standards deviation = square root of (sum of(each no. - mean)^2/n)
=square root of(2257.25/38)
=square root of 59.40
= 7.7
Square root of n= square root of 38
=6.1
Confidence interval =( 95*7.7)/6.1
=119.9
Round off = 120
Confidence interval range= mean+_ confidence interval
=25.5+_120
= 94.5 to 145.5
3). Conclusion
We are 95% confident that the mean HAV angle among such patients is outside this interval.
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