1. Assume a normal distribution for failure strain. Calculate a 99% two-sided co
ID: 3218727 • Letter: 1
Question
1. Assume a normal distribution for failure strain. Calculate a 99% two-sided confidence interval of the mean failure strain. What is the upper limit of the confidence interval?
2. What is the lower limit of the confidence interval?
3. Denote LB as the lower bound of the confidence interval, and UB as the upper bound of the confidence interval. Which of the following is the correct representation of that confidence interval?
4. Assuming that a sample of 100 adults were collected, and the mean failure strain and standard deviation do not change. In order to construct a 97% two-sided confidence interval of the mean failure strain, which change(s) would you need to make?
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biotechnical properties of human nasal periosteum and fasicia. A sample of 15 adults were collected, and it is found that the mean failure strain was 25.0, and the standard deviation was 3.5. Use this information and answer Question 1-4.Explanation / Answer
For a 99% two-sided confidence interval, we get z as 2.575 from the normal tables.
The standard deviation is 3.5 and no. of samples is 15.
Standard error is calculated as z* standard deviation / sqrt(n) = 2.575*3.5/sqrt(15) = 2.32
Upper bound = 25+standard error = 25+2.32=27.32
Lower bound = 25-2.32 = 22.68
Q3) - Options not visible.
Q4) If the no. of samples is 100, we get n = 100 . For 97% interval, z is 2.179. We would change z to 2.179 from 2.575 and n to 100 from 15
Hence standard error would now be 2.179*3.5/sqrt(100) = 0.76265
Confidence interval would now be (24.23735, 25.76265)
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