Silicone implant augmentation rhinoplasty is used to correct

Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 18 (newly deceased) adults, the mean failure strain (%) was 25.0, and the standard deviation was 3.3.

(a) Assuming a normal distribution for failure strain, estimate true average strain in a way that conveys information about precision and reliability. (Use a 95% confidence interval. Round your answers to two decimal places.)

(in percentages)

(b) Predict the strain for a single adult in a way that conveys information about precision and reliability. (Use a 95% prediction interval. Round your answers to two decimal places.)

(in percentages)

Solution

a)
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)=25
Standard deviation( sd )=3.3
Sample Size(n)=18
Confidence Interval = [ 25 ± t a/2 ( 3.3/ Sqrt ( 18) ) ]
= [ 25 - 2.1098 * (0.778) , 25 + 2.1098 * (0.778) ]
= [ 23.359,26.641 ]
95% of the time contain the true value of the population
mean

b)
Predication Interval
CI = x ± t a/2 * (sd* Sqrt(1 + 1/n))
Confidence Interval = [ 25 ± t a/2 ( 3.3 * Sqrt (1 + 1/18) ) ]
= [ 25 ± 2.11 ( 3.3 * Sqrt (1 + 1/18) ) ]
= [ 25 ± 2.11 ( 3.3 * Sqrt (1 + 1/18) ) ]
= [ 25 ± 3.3904 ]
= [ 25 - 3.3904 , 25 + 3.3904 ] = [21.6096, 28.3904]