Question

Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain proportion of circuits are defective because of “undercutting,” which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too narrow. A redesigned process, involving lower pressure in the etching chamber, is being investigated. The goal is to reduce the rate of undercutting to less than 5%. Out of the first 1000 circuits manufactured by the new process, only 34 show evidence of undercutting. Can you conclude that the goal has been met? Find the P-value and state a conclusion.

The P-value is    . Round the answer to four decimal places.

Answer 1

H₀: P > 0.05

H₁:P < 0.05

= 34/1000 = 0.034

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.034 - 0.05)/sqrt(0.05 * 0.95/1000)

                             = -2.32

P-value = P(Z < -2.32)

             = 0.0102

At 0.05 significance level, since the P-value is less than the significance level(0.0102 < 0.05),so we should reject H₀.

So at 5% significance level we can conclude that the goal has been met.