Mock Exam 69122q

Homework 2

ESI 4221C

Due Wednesday 02/11

Exercise 1 A new process has been developed for applying photoresist to 125-mm silicon wafers used in manufacturing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements ( in angstrom x 1000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002. (a) Test the hypothesis that mean thickness is 13.4 x 1000 Å. Use α = 0.05 and assume a twosided alternative. (10 points) (b) Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness is normally distributed. (5 points)

Exercise 2 Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations σ1 = 0.010 liter and σ2 = 0.015 liter, respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles from machine 2 results in average net contents of 2.04 liters and 2.07 liters accordingly. (a) Test the hypothesis that both machines fill to the same net contents, using α = 0.05. What are your conclusions? (10 points) (b) Find the P-value for this test. (5 points)

Exercise 3 An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213–216) describes several experiments investigating the rodding of concrete to remove entrapped air. A 3-in.-diameter cylinder was used, and the number of times this rod was used is the design variable. The resulting compressive strength of the concrete specimen is the response. The data is shown in the following table. Rodding Level

Compressive Strength Observations 10

1530

1530

1440

15

1610

1650

1500

20

1560

1730

1530

25

1500

1490

1510

Is there any difference in compressive strength due to the rodding level? Answer this question by using the analysis of variance (ANOVA) with α = 0.05.

Homework 2

ESI 4221C

Due Wednesday 02/11

Exercise 4 The following data come from sample averages from a process with known mean = 5.92 and known standard deviation of 0.08. The company would really love to have that average for all samples to be equal to exactly 6. Considering only the period of May-August 2014 (4 sampling periods) we obtained the following averages (y column) under the following key factors (average temperature, number of employees, average vacation days per employee). y

Average Temperature

Employees

Vacation Days

6.03

71

100

4

6.07

80

120

1

6.10

90

150

0.5

6.07

87

100

3.5

(a) Use linear regression to predict y for the month of July 2015, assuming the (projected) average temperature is 92, the number of employees is 120 and the expected vacation days is 2.2. (b) Based on the formula you obtained earlier, and assuming that we have no control over the expected temperature at that month (92) and the expected number of vacation days (2.2), how many employees should you hire in order to get as close to 6 (the goal) as possible?