Question

Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens under specified conditions, and the resulting mean and standard deviation were 306.09 newtons and 41.94 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 306.09

sample standard deviation = s = 41.94

sample size = n = 8

Degrees of freedom = df = n - 1 = 7

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,217 = 2.365

Margin of error = E = t/2,df * (s /n)

= 2.365* ( 41.94/ 8)

= 35.068

The 95% confidence interval estimate of the population mean is,

- E < < + E

306.09 - 35.068 < < 306.09 + 35.068

271.022 < < 341.158

(271.022 , 341.158)