Problem 8.20 Statistical analysis of experimental data suggest that the compressive strengths of bricks can be approximated by a normal distribution N(, 2). A new

Problem 8.20 Statistical analysis of experimental data suggest that the compressive strengths of bricks can be approximated by a normal distribution N(µ, σ2). A new (and cheaper) pro[1]cess for manufacturing these bricks is developed whose output is also assumed to be normall distributed. The manufacturer claims that the new process produces bricks whose mean com[1]pressive strengths exceed the standard µ0 = 2500 psi.

(a) Before purchasing these bricks, the customer needs to be convinced that the bricks’ com[1]pressive strength exceeds the standard; that is, the customer wants to test the hypothesis H0 : µ ≤ 2500 against H1 : µ > 2500. Describe in this context the consequences of type I and type II errors.

(b) To test the manufacturer’s claim that the new process exceeds the standard, the compres[1]sive strengths of n = 9 bricks, selected at random, are measured with the following results reported: x = 2600 and sample standard deviation s = 75. Describe the rejection region for testing, at the 5% significance level, your null hypothesis of part (a). State your conclusions.

(c) Test this hypothesis using the confidence interval approach.

(d) Compute the P-value of your test; state your conclusions.