Spring 2002

Dr. McCullough

Name _____________________________________

ID # ______________________________________

Directions :

· Read each problem carefully.

· Do ONLY what the question asks.

· Show all of your work for partial credit.

· No points will be awarded for problems that require work and there is no work.

· Round your answers to four decimal places.

· START EACH NEW PROBLEM ON A SEPARATE SHEET OF PAPER.

· PLEASE BE AS NEAT AS POSSIBLE AND POINT OUT ( CIRCLE ) YOUR FINAL ANSWER IF THERE IS ANY CHANCE THAT I CAN’T FIND IT.

1. ) In semiconductor manufacturing wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic of this process. Two different etching solutions are being evaluated. Eight randomly selected wafers have been etched in each of the solutions and the summary statistics are given below :

Solution 1 Solution 2

a. ) Does the summary information indicate that the claim of both solutions having the same mean etch rate valid at ? Assume equal variances. ( 8 points )

b. ) Construct a 95 % conf interval for the mean etching rate of Solution 1. ( 6 points )

c. ) Construct a 95 % confidence interval for the ratio of solution 1 variance to solution 2 variance, . ( 6 points )

2. ) An experiment is to be run to test the effects of nitrogen fertilizer on lettuce production. Five rates ( 0, 50, 100, 150, 200 ) of ammonium nitrate were applied to the plants. There will be 4 replicates.

a. ) What type of design structure is explained above. ( 5 points )

b. ) Construct the source column and the degrees of freedom column for the ANOVA table. ( 8 points )

3. ) Now, consider the experiment in question # 2 with the following change :

An experiment is to be run to test the effects of nitrogen fertilizer on lettuce production. Five rates ( 0, 50, 100, 150, 200 ) of ammonium nitrate were applied to the plants. There will be 4 very different plots of land ( that you can assume will hold multiple lettuce plants ) in which the fertilizer has to be tested on.

a. ) What type of design structure is explained above. ( 5 points )

b. ) Construct the source column and the degrees of freedom column for the ANOVA table. ( 8 points )

4. ) An experiment was performed to compare the effects of cues on speed of response of a human subject. A personal computer was used to present a stimulus to a subject, and the reaction time required for the subject to press a key was monitored. Times selected for the experiment were 5, 10, and 15 seconds. Each stimulus type, auditory and visual, was used with each of the three times for six levels of the treatment being investigated. Three independent subjects were selected for each stimulus type and time combination.

Source df Sum of Squares Mean Square F-value Probability

Treatment *** 0.0255489 *** *** ***

Error 12 0.0034720 0.0002893

Total *** 0.0290209

Level of Treatment n Mean Standard Deviation

1 auditory, 10 seconds 3 0.17866667 0.01040833

2 auditory, 15 seconds 3 0.21200000 0.02088061

3 auditory, 5 seconds 3 0.18500000 0.01734935

4 visual, 10 seconds 3 0.25933333 0.02400694

5 visual, 15 seconds 3 0.26500000 0.01389244

6 visual, 5 seconds 3 0.26833333 0.01101514

a. ) Supply the missing numbers to the ANOVA table for the blanks above that contain the symbol ( *** ) . ( 12 points )

b. ) Write a contrast that would test for a difference between the mean of the stimulus types . Make sure and clearly label the means and values for the contrast. (6 pts)

c. ) Compare the six treatment means using Tukey’s test (method). Use . Write the appropriate conclusion for the test. ( 10 points )

5. ) An animal physiologist studied the pituitary function of hens put through a standard regimen used by egg producers. The five stages of the regimen were premolt, fasting, 60 grams of bran, 80 grams of bran, and laying mash. The study was to try to determine why hens come back into production after the forced molt. One of the compounds measured was serum T₃ concentration. There originally were 5 hens in each group but some were lost during the course of the experiment. The data in the table are the serum T₃ measurements for the hens that were sacrificed at the end of each stage of the regimen.

Treatment Serum T₃concentration

Premolt 94.09, 90.45, 99.38, 73.56

Fasting 98.81, 103.55, 115.23, 129.06, 117.61

60 g bran 197.18, 207.31, 177.50

80 g bran 102.93, 117.51, 119.92, 112.01, 101.10

laying mash 82.94, 83.14, 89.59, 87.76

a. ) Compute the analysis of variance to look for a different in treatment means at significance level. Write out the ANOVA table. ( 20 points )

b. ) Estimate the overall mean and treatment effects. ( 12 points )