Question

Is there a main effect of product weight on consumers attitude towards the product (at a significance level of .05)

Select one:

a. yes, product weight has a significant main effect

b. no, product weight does not have a significant effect

c. Not enough information to reach a conclusion

Before finalizing the design of a keyboard, an electronics company decided to conduct an experiment to see the effect of two design choices (backlight: red vs. blue; product weight: heavy vs. light) on customers' attitude towards the product (measured on a scale of 1 to 7). Run the appropriate statistical test and at .05 level identify whether these design choices have an effect on consumers' attitude towards the product. Identify if there is a significant interaction effect (at .05 level).
	blue	red
heavy	1	7
	7	7
	5	6
	5	7
	5	7
	1	7
	3	7
	7	6
	3	7
	7	6
	2	7
	3	4
	1	6
	7	6
	7	7
	4	7
	5	5
	5	6
	4	5
	5	6
light	7	6
	7	7
	5	4
	7	6
	5	7
	5	6
	5	3
	4	4
	6	3
	7	4
	5	6
	6	3
	6	7
	5	7
	6	4
	5	6
	5	7
	7	5
	5	7
	4	4

Answer 1

Soln

Option b ie No, product weight does not have a significant effect

Null and Alternative Hypothesis:

We will have three hypotheses:

Weight

H₀: µ_Heavy = µ_Light

H₁: Not all Means are equal

Colour

H₀: µ_Blue = µ_Red

H₁: Not all Means are equal

Interaction

H₀: An interaction is absent

H₁: Interaction is present

Alpha = 0.05

Degress of Freedom:

Df_Weight(A) = a-1 = 2-1 = 1

Df_Colour (B) = b-1 = 2-1 = 1

df _{Weight * Colour} (A*B) = (a-1) * (b-1) = 1*1 = 1

df _error = N – ab = 80 – 2*2 = 76

df _total= N – 1 = 80 – 1 = 79

Decision Rule (3):

We have three hypotheses, so we have three decision rules:

Critical Values:

Weight (df_Weight(A), df _error): (1,76) = 3.97

Colour (df_Colour (B),df _error): (1,76) = 3.97

Interaction (df _{Weight * Colour} (A*B), df _error) : (1,76) = 3.97

[Weight] If F is greater than 3.97, reject the null hypothesis

[Colour] If F is greater than 3.97, reject the null hypothesis

[Interaction] If F is greater than 3.97, reject the null hypothesis

Test Statistics:

SS_Weight = ∑(∑a_i)²/b*n - T²/N = 0.31

SS_Colour = ∑(∑b_i)²/a*n - T²/N = 13.61

SS_{Weight*Colour} = ∑(∑a_i * b_i)²/n - ∑(∑a_i)²/b*n - ∑(∑b_i)²/a*n + T²/N = 25.31

SS_Total = ∑(Y)² - T²/N = 198.99

SS_Error = SS_Total - SS_Weight - SS_Colour - SS_{Weight*Colour} = 159.75

MS = SS/df

               

F = MS_effect / MS_error

Hence,

F_Weight = 0.31/2.10 = 0.15

F_Colour = 13.61/2.10 = 6.48

F_Interaction = 25.31/2.10 = 12.04

Source of Variation	SS	df	MS	F
Weight	0.31	1	0.31	0.15
Colour	13.61	1	13.61	6.48
Interaction	25.31	1	25.31	12.04
Error	159.75	76	2.10
Total	198.99	79

Results:

[Weight] If F is greater than 3.97, reject the null hypothesis

Our F = 0.31, we fail to reject the null hypothesis.

[Colour] If F is greater than 3.97, reject the null hypothesis

Our F = 13.61, we reject the null hypothesis.

[Interaction] If F is greater than 3.97, reject the null hypothesis

Our F = 25.31, we reject the null hypothesis.