35. A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.48 MPa and a sample standard deviation of .79 MPa ( Characterization of Bearing Strength...

35.
A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.48 MPa and a sample standard deviation of .79 MPa ( Characterization of Bearing Strength Factors in Pegged Timber Connections,
J. Struct. Engrg., 1997: 326—332).

a.
Calculate and interpret a 95% lower con dence bound for the true average proportional limit stress of all such joints. What, if any, assump- tions 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.