Silicone implant augmentation rhinoplasty is used to correct congenital nosedeformities. The success of the procedure depends...
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. The article "Biomechnics in Augmentation Rhinoplasty" reported that for a sample of 15 (newly deceased) adults, the mean failure strain (%) was 25.0, and the standard deviation was 3.5. (p. 277 #35) a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability. b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solutions
Expert Solution
Concepts and reason
Confidence intervals: A confidence interval provides a range of values which is likely to contain the population parameter of interest.
The population standard deviation is unknown and the sample size is less than 30 use one sample t -test.
Fundamentals
The formula for confidence interval for single mean is as shown below:
xˉ−tα/2,n−1(ns)<μ<xˉ+tα/2,n−1(ns)
Here xˉ is the sample mean, s is the standard deviation, μ is the population mean, tα/2,n−1 is the critical value and n is the sample size.
The formula for prediction interval is as shown below:
xˉ−tα/2,n−1s1+n1<μ<xˉ+tα/2,n−1s1+n1
The formula for degrees of freedom is, df=n−1
(a)
The available information is n=15,xˉ=25ands=3.5
The degrees of freedom is,
df=n−1=15−1=14
From the t-distribution tables, the critical value at 5% level of the significance for 14 degrees of freedom about two tailed is 2.145.
The confidence interval estimate of true mean is as shown below:
From the result of part (a), the difference between upper and lower limit is approximately 4. In part (b), the difference between the upper and the lower limit is approximately 16.
Therefore, from this it can be said that the prediction interval is roughly four times as wide.
Ans: Part a
The confidence interval for the true mean is (23.0616,26.9384).
Part b
The prediction interval for the true mean is (17.2463, 32.7537).
The prediction interval is roughly four times as wide.
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. A sample of 30 (newly deceased) adult rhinoplasty
patients had a mean failure strain (%) of 28.2 and a standard
deviation of 4.1.
a Calculate a 90% confidence interval for the true mean failure
strain for all rhinoplasty patients.
b Based on your confidence interval in part a, is it plausible
that...
1a. 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 17 (newly
deceased) adults, the mean failure strain (%) was 26.0, and the
standard deviation was 3.1.
(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...
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 20 (newly deceased) adults, the mean failure strain% was 26.0, and the standard deviation was 3.5. (a) Assuming a normal distribution or failure strain, estimate true average strain in a way that conveys information about precision and reliability. confidence interval. Round your answers to two...