Question

Suppose you own a factory. You want to determine whether the level of illumination on the assembly line affects worker productivity. One day, you have one group of 5 employees work under very dim lighting, a second group of 5 employees work under a moderate level of light, and a third group of 5 employees work under very bright lights. The mean productivity (number of units assembled) for the low light group was 56; for the moderate light group, 68; for the bright light group, 60.

a) State the appropriate null and alternative hypotheses

b) Complete the following source table describing the results of an ANOVA testing the significance of the difference between the sample means for α = .05.

c) What is the critical value of F?

d) On the basis of these results, would you reject or fail to reject H₀?

e) What does this mean in terms of the alternative hypothesis?

Source	df	SS	MS	F
Between		124.8
Within		189.8
Total

Answer 1

a] NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha: Not all means are equal.

b]

SOURCE	DF	SS	MS	F
BETWEEN	3-1=2	124.8	62.4	3.944
WITHIN	14-2=12	189.8	15.82
TOTAL	n-1=15-1=14

c] Degrees of freedom 1= 2

degrees of freedom 2= 12

level of significance= 0.05

Critical value of F= 3.74

d] Since Critical value of F is SMALLER THAN F CALCULATED THEREFORE SIGNIFICANT

DECISION: REJECT NULL HYPOTHESIS H0.

e] CONCLUSION: WE HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT NOT ALL MEANS ARE EQUAL AT 0.05 LEVEL OF SIGNIFICANCE