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.2922163218282315293523223722492616232633282025303219332421382622301120232124It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Given a 95% confidence interval for the mean HAV angle in the population of all such patients, find the following.x (mean) = s=(standard deviation) = Confidence Interval: ° to ° Conclusion1) We are 95% confident that the mean HAV angle among such patients is within this interval.2) We are 95% confident that the mean HAV angle among such patients is outside this interval. 3) The mean HAV angle among such patients will always be outside this interval 95% of the time.4) The mean HAV angle among such patients will always be within this interval 95% of the time. 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.29221632 2318 1528 29Confidence Interval:o to37352322 4922O263323 280261620 3225 1930 33It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Given a 95% confidence interval for the mean HAV angle in the population of all such patients, find the following.x = 25.8158s = 7.410226241121 22 2038 30 232124ConclusionO We are 95% confident that the mean HAV angle among such patients is within this interval.O We are 95% confident that the mean HAV angle among such patients is outside this interval.O The mean HAV angle among such patients will always be outside this interval 95% of the time.O The mean HAV angle among such patients will always be within this interval 95% of the time.

n= 38 Sample size We need to find the 95% confidence interval for the population mean

Answered: HAV is a deformation of the big toe…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

29
22
16

32
18
28

23
15
29

35
23
22

37
22
49

26
16
23

26
33
28

20
25
30

32
19
33

24
21
38

26
22
30

11
20
23

21
24

It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Given a 95% confidence interval for the mean HAV angle in the population of all such patients, find the following.

x (mean) =

s=(standard deviation) =

Confidence Interval:
° to °

Conclusion

1) We are 95% confident that the mean HAV angle among such patients is within this interval.

2) We are 95% confident that the mean HAV angle among such patients is outside this interval.

3) The mean HAV angle among such patients will always be outside this interval 95% of the time.

4) The mean HAV angle among such patients will always be within this interval 95% of the time.

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.
29
22
16
32 23
18 15
28 29
Confidence Interval:
o to
37
35
23
22 49
22
O
26
33
23 28
0
26
16
20 32
25 19
30 33
It is reasonable to regard these patients as a random sample of young patients who require HAV surgery. Given a 95% confidence interval for the mean HAV angle in the population of all such patients, find the following.
x = 25.8158
s = 7.4102
26
24
11
21 22 20
38 30 23
21
24
Conclusion
O We are 95% confident that the mean HAV angle among such patients is within this interval.
O We are 95% confident that the mean HAV angle among such patients is outside this interval.
O The mean HAV angle among such patients will always be outside this interval 95% of the time.
O The mean HAV angle among such patients will always be within this interval 95% of the time.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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