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Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809

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BuyFindarrow_forward

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809
Textbook Problem

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 “Biomechanics in Augmentation Rhinoplasty” (J. of Med. Engr. and Tech., 2005: 14–17) reported that for a sample of 15 (newly deceased) adults, the mean failure strain (%) was 25.0, and the standard deviation was 3.5.

  1. a. Assuming a normal distribution for failure strain, estimate true average strain in a way that conveys information about precision and reliability.
  2. 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)?

a.

To determine

Obtain the estimate for population mean failure strain of silicone implant augmentation rhinoplasty.

Explanation

Given info:

The success rate of the silicone implant augmentation rhinoplasty depends on various biochemical properties of human nasal periosteum and fascia. A medical journal reported that for a sample of 15 adults the mean failure strain is x¯=25.0% and s=3.5%.

Calculation:

The following assumptions are required for the confidence interval about mean using t-distribution to be valid.

Requirements for t-distribution to construct confidence interval about mean:

  • The sample must be drawn using simple random sampling.
  • The population standard deviation is unknown.
  • Either the population must be approximately normal or the sample size must be greater than 30.

Thus, the requirements must be satisfied for the confidence interval about mean using t-distribution to be valid.

Here, the sample is drawn randomly and the population standard deviation is unknown.

Moreover, it is given that the distribution of the population of failure strain of silicone implant augmentation rhinoplasty is normal.

For the confidence interval using t-distribution to be valid, an assumption about normality of population has to be made.

Since, the sample is not greater than 30.

Therefore, t-distribution is valid in constructing confidence interval about mean

b.

To determine

Find and interpret the 95% prediction interval for the failure strain of silicone implant augmentation rhinoplasty for a single adult.

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