In an experiment involving the breaking strength of a certai

In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were Find a 99% confidence interval for the difference in the mean strengths between threads treated for 60 seconds and those treated for 120 seconds. Round the degrees of freedom down to the nearest integer, the sample standard deviations to six decimal places, and your final answers to four decimal places each. The confidence interval is .

Solution

60 seconds: n1=10, xbar1=50.8, s1=5.329165

120 seconds: n2=10, xbar2=59.7, s2=5.329165

The degree of freedom = n1+n2-2=10+10-2=18

Given a=1-0.99=0.01, t(0.005, df=18) =2.88 (from student t table)

So the lower bound is

(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)

=(50.8-59.7)-2.88*sqrt(5.329165^2/10+5.329165^2/10)

=-15.7638

So the upper bound is

(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)

=(50.8-59.7)+2.88*sqrt(5.329165^2/10+5.329165^2/10)

=-2.0362