Question

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 the true mean failure strain is 30%?

c Conduct a hypothesis test at the 0.01 level to determine if the true mean failure strength is 30%.

d Does your conclusion in part c match your answer in part b? Should it?

Answer 1

Here

sample mean

sample standard deviation

and sample size n = 30

a) a 90% confidence interval for the true mean failure strain for all rhinoplasty patients

b) Based on the 90% confidence interval, since upper bound of the confidence interval < 30, so it is not plausible that the true mean failure strain is 30%.

c) The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 1% level of signfiicance if P-value < 0.01

Now,

The value of the test statistic

P-value

Since P-value > 0.01, so we fail to reject H₀ at 1% level of signfiicance and we can conclude that the true mean failure strength is not significantly different from 30%.

d) Since P-value < 0.10, so we reject H₀ at 10% level of signfiicance and we can conclude that the true mean failure strength is significantly different from 30%.