Asample 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 0.79 mpa ("characterization of bearing strength factors in pegged timber connections," j. of structural engr., 1997: 326332).
a. calculate and interpret a 9596 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 .