A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.47 MPa and a sample standard deviation of 0.74 MPa.
(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type.
Confidence and Prediction Interval:
The t distribution with (n-1) degree of freedom is used to construct the 95% confidence interval and the 95% prediction bound. The prediction interval is used in the regression analysis and the confidence interval is used for the estimate of the population parameter.