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 n = 32 specimens under specified conditions, and the resulting mean and standard deviation were 302.89 Newtons and 41.47 Newtons, respectively.

Construct an "approximate" 95% confidence interval for the true average breaking force of the acrylic bone cement under the specified conditions, using t-critical = 2 as the approximate critical value.


Lower endpoint:  Upper endpoint:  

Answer 1

Solution :

Given that,

= 302.89

s = 41.47

n = 32

Degrees of freedom = df = n - 1 = 32 - 1 = 31

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,31 = 2.  

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

= 2 * (41.47 / 32)

= 14.66

Margin of error = 14.66

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

- E < < + E

302.89 - 14.66 < < 302.89 + 14.66

288.23 < < 317.55

Lower endpoint: = 288.23

Upper endpoint: = 317.55