Prestressed wire wrapping concrete pipe is manufactured in large rolls. A quality-control inspection requires 5 specimens from a roll to be tested for ultimate tensile strength (UTS). The UTS measurements (in 1000 psi) turned out to be 253, 261, 258, 255, 256.
a) Use these data to construct a 95% confidence interval estimate of the true mean UTS for a sample roll. What assumption you have assumed?
b) Calculate and interpret a 95% prediction interval for a new specimen selected at random from the roll.