Give the correct answer with correct DECIMAL PLACES, don\'t just copy a solution

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Give the correct answer with correct DECIMAL PLACES, don't just copy a solution from previously answered questions...

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 (96) was 25.0. 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 two decimal places.) use a 95% confidence interval Round your answers to (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.) How does the prediction compare to the estimate calculated in part (a)? The prediction interval is much wider than the confidence interval in part (a) The prediction interval is much narrower than the confidence interval in part (a). The prediction interval is the same as the confidence interval in part (a).

Explanation / Answer

Mean failure strain xstrain= 25.0 %

standard deviation sstrain= 3.1 %

a) 95% confidence interval =   xstrain +- tn-1, /2 (sstrain/n)

= 25 +- t16, 0.025 (3.1/17)

= 25 +- 2.120 * 0.7519

= (23.41%, 26.59%)

(b) 95% prediction interval = xstrain +- tn-1, /2 (sstrain * sqrt(1 + 1/n) )

= 25.0 +- t16,0.025 * 3.1 * sqrt(1 + 1/17)

= 25.0 +- 2.120 * 3.1 * 1.029

= (18.24%, 31.76%)

OPtion a is correct as the prediction interval is much wider than the confidence interval in a.

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