Question

3. Suppose that a toy manufacturer developed 2 toys for the new season. Four different brands  

    of batteries are uses in each of the 2 toys. The life of the toys with different batteries was analyzed.  

MINITAB results are presented.  Two measurements were taken for each brand of batteries used on the 2 toys.  Please: USE the P-Values, NOT F Tables.

Each toy will be sold equipped with the specific battery which lasted the longest.

What design should be used?  Circle the one you would use:

ONE WAY                      TWO WAYS Block               TWO WAYS with Interaction, (Factorial)

        ………………………………………………………………………………………………

Complete the table ONLY for the design you have selected above

(ONEWAY) :  Source  Brands

Source    DF     Adj SS     Adj MS     F-Value     P-Value

Brands            104.0                             0.079

Error                        12.00

Total     15      248.0

(TWO WAY Non Interaction) : Sources    Brands and Toys

Source    DF      Adj SS     Adj MS     F-Value    P-Value

Brands            104.00                            0.023

Toys                          64.00                 0.013

Error                         7.273

Total     15      248.00

(TWO WAY With  Interaction) : Res versus A  and  B + Interaction

Source  DF        Adj SS     Adj MS      F-Value    P-Value

  A               104.00                             0.013

  B                           64.00                  0.007

  A*B              40.00                             0.119

Error                         5.000

Total   15        248.00

USE ANOVA TO ANSWER THESE QUESTIONS, (Use α = 0.05).  

Are the Batteries performing equally or do they show differences?………………..

State the Alternate Hypothesis for Batteries:  Ha : …………………………………….

How many degrees of freedom for Batteries?…….

What is the value for  MS  for Batteries?………                  And  the  F statistic?……

If you selected BLOCK or FACTORIAL designs, answer the following questions:

Are the Toys performing equally or do they show differences?………………..

State the Alternate Hypothesis for Toys:  Ha : …………………………………….

How many degrees of freedom for Toys?…….

What is the value for  SS  for Toys?………                  And  the  F statistic?……

If you selected Factorial design, is the INTERACTION  statistically significant?……………….

How many degrees of freedom for the INTERACTION?……...

Answer 1

What design should be used? TWO WAYS with Interaction, (Factorial)



Are the Batteries performing equally or are they showing differences? They are showing differences.
: the measurement of at least one of the 4 brands of batteries is different.
Degrees of freedom = 3.
MS = 34.67, F statistic = 6.93.

Are the Toys performing equally or are they showing differences? They are showing differences.
: the measurement of at least one of the 2 brands of toys is different.
Degrees of freedom = 1.
SS = 64.00, F statistic = 12.8.

Is the Interaction statistically significant? No, it is not statistically significant.
Degrees of freedom for Interaction = 3.