Question

A company is considering purchasing wine glasses from 1 of 4 possible manufacturers (identified as Manufacturer A, Manufacturer B, Manufacturer C, and Manufacturer D). The cost of the wine glasses is the same for each manufacturer, so the company is conducting a test to determine if there is a difference in the average life of glasses produced by the manufacturers. Four (4) glasses are randomly sampled from each manufacturer and the glasses are tested until they break. A partially completed ANOVA table of the results is shown below. The F critical value is shown for α = 0.05.

ANOVA
Source of Variation	SS	df	MS	F	F crit
Between Groups	204993	3			3.4903
Within Groups	78218
Total	283211	15

1. State the Null and alternative hypotheses of interest.

Ho: __________________________________________

H_A: __________________________________________

2. Compute the mean squares for the between groups: __________________
3. Compute the mean squares for the within groups: ____________________
4. What is the calculated value of the F test statistic: ____________________
5. Based on the calculated value and critical value of F what conclusion do you reach concerning whether the manufacturer has an effect on the average life of the wine glasses?

Answer 1

Explanation:-

Given the partially data ANOVA table

source of Variation	sum of squares	degrees of freedom	mean squares	tabulated value F
Between groups	204993	3	-	3.49
within groups	78213	-	-
Total	283211	15	-

Step(i):-

Mean of squares between groups

=

=

Mean of squares between within groups

=

  

=   

Step(ii):-

Now Complete ANOVA table

source of Variation	sum of squares	degrees of freedom	mean squares	critical value F
Between groups	204993	3	68,331	3.49
within groups	78213	12	6518.16
Total	283211	15	74,849.16

a)

Null hypothesis:- H0: The manufacturer has do not effect on the average life of the wine glasses

Alternative hypothesis:H1: The manufacturer has effect on the average life of the wine glasses

b) Mean of squares between groups = 68,331

c)    Mean of squares within groups = 6518.16

d) F-statistic

  

  

the critical value F(3 , 12 ) = 3.49

Conclusion:-

The calculated value F = 10.48 > the critical value 3.49

Null hypothesis is rejected

Alternative hypothesis is accepted

The manufacturer has effect on the average life of the wine glasses