A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.50 MPa and a sample standard deviation of .80 MPa.
a. Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. What, if any, assumptions did you make about the distribution of proportional limit stress?
b. Calculate and interpret a 95% lower prediction bound for the proportional limit stress of a single joint of this type.

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The Answer of A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.50 MPa and a sample standard deviation of .80 MPa.
a. Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. What, if any, assumptions did you make about the distribution of proportional limit stress?
b. Calculate and interpret a 95% lower prediction bound for the proportional limit stress of a single joint of this type.

A Sample of 14 Joint Specimens of a Particular Type