Question

Acrylic bone cement is sometimes used in hip and knee replacements to secure an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens, and the resulting mean and standard deviation were 306.01 newtons and 41.92 newtons, respectively. Assuming that it is reasonable to believe that breaking force has a distribution that is approximately normal, use a 95% confidence interval to estimate the mean breaking force for acrylic bone cement. (Use a table or technology. Round your answers to three decimal places.)

( , ) N

Answer 1

Solution :

Given that,

= 306.01

s =41.92

n = 8

Degrees of freedom = df = n - 1 = 8- 1 =7

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t _/2,df = t_0.025,7 = 2.365 ( using student t table)

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

=2.365 * (41.92 / 8)

E= 35.052

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

- E < < + E

306.01 -35.052 < < 306.01+ 35.052

270.958< < 341.062

( 270.958,341.062 )