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PROBLEM #1 Suppose Henry’s Caps and Tops has designed a new Spring Break shirt with a...

PROBLEM #1

Suppose Henry’s Caps and Tops has designed a new Spring Break shirt with a choice of four different marine life on the back of the shirts.  His marketing managers would like to conduct a test to determine the customers’ preferences of marine life.  Six people were asked to look at the designs and rate each design on a scale of 1-20.  The results are as follows:

Marine Life

Person

Shark

Turtle

Dolphin

Manatee

1

19

20

12

17

2

18

17

17

18

3

17

18

16

19

4

13

19

12

14

5

10

13

7

18

6

13

12

11

16

The table below represents the partial results of a Random Block ANOVA computed in Excel
using an α = 0.05.  

Use the table as your guide to calculate the missing values requested in the following questions.

Source

Sum of

Squares

Degrees of

Freedom

Mean Sum of

Squares

F

P-value

F crit

Column/

Treatments

73.5

3

0.0175

Row/Blocks

117.5

5

0.0111

Error

Total

270.5

23

  1. The Sum of Squares Error (SSE) for this ANOVA procedure is __________.

  1. The total number of observations (nT) for this ANOVA procedure is __________.

  1. The degrees of freedom for the sum of squares error for this ANOVA procedure is ______________.
  1. The Mean Square between Treatments (MSTR) for this ANOVA procedure is __________.

  1. The Mean Square Block (MSBL) for this ANOVA procedure is __________.

  1. The Mean Square Error (MSE) for this ANOVA procedure is __________.

  1. The number of main treatments / populations being compared for this ANOVA procedure is __________.

  1. The number of blocks being compared for this ANOVA procedure is __________.

  1. The main treatment F-test statistic for this ANOVA procedure is ________.

  1. Using α = 0.05, the critical F-score for the main factor for this ANOVA is ________.

  1. Setup the appropriate main treatment Hypothesis test

H0:

HA:

  1. Using all the data above, interpret the results

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