Acrylic bone cement is commonly used in total joint replacement to secure the ar
ID: 3225961 • Letter: A
Question
Acrylic bone cement is commonly used in total joint replacement to secure the artificial joint. Data on the force (measured in Newtons, N) required to break a cement bond was determined under two different temperature conditions and in two different mediums appear in the following table.
(a) Estimate the difference between the mean breaking force in a dry medium at 37 degrees and the mean breaking force at the same temperature in a wet medium using a 90% confidence interval. (Round your answers to one decimal place.)
( , )
(b) Is there sufficient evidence to conclude that the mean breaking force in a dry medium at the higher temperature is greater than the mean breaking force at the lower temperature by more than 100 N? Test the relevant hypotheses using a significance level of 0.10. (Use higher temperature lower temperature. Round your test statistic to two decimal places. Round your degrees of freedom to the nearest whole number. Round your p-value to three decimal places.)
Explanation / Answer
a) x1 = 311.8 , x2 = 355.58 , s1 = 18.298 , s2 = 27.269 , n1 = n2 = 6
t value at 90% CI = +/- 1.812
CI = (x1 - x2) + /- t * sqrt ( s1^2 / n1 + s2^2 / n2)
= ( 311.8 - 355.58) + / -1.812 ( 18.298^2/6 + 27.269^2/6)
= (68.1 , -19.5)
b )
Null hypothesis: 1 - 2 <= 100
Alternative hypothesis: 1 - 2 >100
Test statistic:
x1 = 311.8 , x2 = 157.48 , s1 = 18.298 , s2 = 44.358
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt [(18.298^2 / 6) + (44.358^2/6)]
= 19.589
t = [ (x1 - x2) - d ] / SE
= [(311.8- 157.48) - 100] / 19.589
= 2.77
df = 6 + 6 - 2 = 10
p value is calculated using t = 2.77 , df =10
p value = .009894.
We reject the null hypothesis. p value is less than 0.10
there is sufficient evidence.
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