Question 5.21: A sample of 10 concrete blocks manufactured by a certain pro......

For a 95% prediction interval, 𝛼 = 0.025. We have a sample size of n = 10, so we consult the Student’s t table (Table A.3) to find t_{9,.025} = 2.262. Using expression (5.19)

\overline{X} ± t_{n-1,α/2} s \sqrt{1 + \frac{1}{n}}      (5.19)

with \overline{X} = 1312 and s = 25, the 95% prediction interval is 1312 ± 2.262(25)\sqrt{1 + 1 ∕ 10}, or (1253, 1371).