Your Teac ilicone implant augmentation thineplasty is used to correct congenital

Question

Your Teac ilicone implant augmentation thineplasty is used to correct congenital nose deformities. The success of the precedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 17 (newly deceased) adas, the mean fare stran (%) was 2.0, and the ta dard drdato (a) Assuming a normal distribution for failure tran estimate true average strain in a way that conveys information about prechen and reLtity. (Uw·95% erlence itinil Roand your aniere to two decimal places) (b predict "be "rain for a sin e adut in a way that conve" int rmation about pre-and relatin. -·95% p adaan l ieve Rmnd m-ane -to be. de ind place. How does the prediction compare to the estimate calculated in part (a)? O The prediction interval is much wider than the confidence interval in part (a). O The prediction interval is much narrower than the confidence interval in part (a) O The prediction isterval is the same as the confidence interval in part (a)

Explanation / Answer

(a) (1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=26±t(0.05/2, 17-1)*3.2/sqrt(17)=26±2.12*3.2/sqrt(17)

=26±1.65=(24.35,27.65)

(b) 95% prediction interval for sample mean=mean±t(.05/2,4)*sd*sqrt(1+1/n)=26±2.12*3.2*sqrt(1+1/17)

=26±6.98=(19.02,32.98)

right choice is (first) prediction interval is much wider than confidence interval in part (a)

=26±

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