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

ANOVA
Source of Variation	SS	df	MS	F	F crit
Between Groups	204993	3	68331	10.48316	3.4903
Within Groups	78218	12	6518.167
Total	283211	15

Hypothesis:

H0: μ1 = μ2 = μ3 = μ4

Ha: Not all μ's same

the mean squares for the between groups = SSB/dfB = 68331

the mean squares for the within groups = SSW/dfW = 6518.167 (dfW = dfT-dfB)

the calculated value of the F test statistic = MSB/MSW = 10.48316

Conclusion:

F stat > F critical, Reject H0

Therefore, there is enough evidence to conclude that there is a difference in the average life of glasses produced by the manufacturers.