In: Statistics and Probability
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.
Temperature | Medium | Data on Breaking Force |
22 degrees | Dry | 100.7, 142.7, 194.8, 118.4, 176.1, 213.1 |
37 degrees | Dry | 302.2, 338.3, 288.8, 306.8, 305.2, 327.5 |
22 degrees | Wet | 385.4, 367.2, 322.6, 307.4, 357.9, 321.4 |
37 degrees | Wet | 363.8, 376.6, 327.7, 331.9, 338.1, 394.6 |
(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 μhigher temperature −
μlower 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.)
t | = | |
df | = | |
P | = |