Question

4.12 Yaschchin (1995) discusses a process for the chemical etching of silicon wafers used in integrated circuits. This company wishes to detect an increase in the thickness of the silicon oxide layers because thicker layers require longer etch- ing times. Process specifications state a target value of 1 micron for the true mean thickness. Historically, the layer thickness have a standard deviation of 0.06 micron. a. A recent random sample of four wafers yielded a sample mean of 1.134. Conduct a hypothesis test to determine whether the true mean thickness has increased. Use a significance level of 0.05. b. Find the p-value associated with the test in part a.

Answer 1

@ Given that - X = 1.134 o = 0.06 n=4 To test the hypothesis, Hoi l = 1 H,: MX1 ( claim) Test statistics, o is known 2=X-4 - 1.134-) 5/55 0.0/57 = 0.134 0.03 2=4.47 The critical value, Zx = 1.645 Here, z> Zd, we Reject Ho at 57. level. There is sufficient evydance to support that true mean thickness has increased. L P-value = Plz>4:47] using z table, P-value = 10.00001