statistics studies

Homework 19

Due Monday Nov 20 ( 3 5 P o in t s )

Problem 1) Three different machines are being considered for use in manufacturing rubber seals. The machines are being compared

with respect to tensile strength of the product. A random sample of four seals from each machine is used to determine whether the

mean tensile strength varies from machine to machine.

Observations

Machines 1 2 3 4

A 10 9 17 11

B 15 15 20 18

C 14 20 12 19

The null hypothesis is 𝜏𝐴 = 𝜏𝐵 = 𝜏𝐶. The alternate hypothesis is that at least one machine is different.

1) Generate the ANOVA table for the test. (15 points) (Hint: You can use Example 13-1 as a guide)

2) Comment on whether to accept or reject the null hypothesis. (5 points) Remember, you will use the F-table (in the back of

your textbook or google an F table online).

Problem 2)

Using Yates, fill in the design matrix in standardized order for a 2 level, 4 factor experiment. (7OV points)

This is called a 24 experiment (four factors, each at 2 levels)

Experiment A B C

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Problem 3) Assume you are investigating the effects of Stirring Rate and Temperature on Filtration Rate. You ran a single replicate

(one experiment) at each of the following settings. Compute the effects of A, B, and the interaction AB (just like we did in class on

the ‘eye-hand’ coordination test). (8 points)

A (Stirring Rate) B (Temperature) AB Response (Filtration Rate)

1 - - + 43

2 + - - 64

3 - + - 49

4 + + + 68