Question

4. 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 27.5 and a standard deviation of 4.3. Perform a hypothesis test to determine if the true mean failure strain for all adult rhinoplasty patients exceeds 25%.

a What hypotheses should be tested?

b What is the test statistic value?

c What is the p-value?

d Make a conclusion in terms of the problem.

Answer 1

Given that, sample size (n) = 30, sample mean = 27.5% and sample standard deviation (s) = 4.3%

a) Claim : μ > 25%

Null Hypothesis : H0 : μ = 25%

Alternative Hypothesis : Ha : μ > 25%

b) Test statistic is,

=> Test statistic = 3.184

Degrees of freedom = 30 - 1 = 29

Using Excel we find the p-value as follows :

Excel Command : =TDIST (3.184, 29, 1) = 0.0017

=> P-value = 0.0017

d) Reject the null hypothesis, since p-value is less than 0.05 level of significance.

Conclusion : There is sufficient evidence to conclude that the true mean failure strain for all adult rhinoplasty patients exceeds 25%.