A sample of 17 joint specimens of a particular type gave a sample mean proportio

Question

A sample of 17 joint specimens of a particular type gave a sample mean proportional limit stress of 8.54 MPa and a sample standard deviation of 0.71 MPa.(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. MPa Interpret this bound. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.

Explanation / Answer

a) 95% c.i=Xbar+-tn-1*SE(Xbar), where Xbar is sample mean, SE(Xbar) is standard error of mean, tn-1 is critical t at n-1 degrees of freedom at alpha=0.05.

SE(Xbar)=s/sqrt n, where s is sample standard deviation, n is sample size.

=8.54+-2.120(0.71/sqrt 17)

=8.17 to 8.91

Lower confidence bound is 8.17

Option A)

Option C)

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