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Practice Problems

A company has three machines that fill 350 mL cans with pop

For the theory section, show your work and do not round off your middle work. 

Keep your final answer to four (4) decimal places, where relevant.
1. A company has three machines that fill 350 mL cans with pop. The quality control inspector is interested in knowing whether the average fill for the three machines is the same. The following data represent random samples of fill measurements (in mL) for 15 cans of pop filled by different machines:
Machine A Machine B Machine C
346                     347             351
353                     346             352
351                     343             352
342                     348             354
                    351             356
a. Conduct an analysis of data and summarize the result in an AOV table. [Assume that all necessary conditions are satisfied.]
b. Test the research hypothesis that there is a difference in the mean fill of the three machines.
c. Regardless of your answer for part b, use Tukey’s W procedure to determine pairwise differences in the three machines.
d. Is there significant evidence that machines A and B combined produced lower mean fills that the mean fill of machine C?  (Hint:  Please see Unit 2 material about linear contrasts.)
e. Assume the assumptions of normality and/or equal variance are violated here.  What are alternative method of analysis that could be used? 

2. In a completely randomized design, 19 experimental units were used for the first treatment, 12 experimental units for the second treatment and 22 experimental units for the third. Part of the AOV table for this experiment is given below. 
Source SS df MS F
Treatment ? ? 4
Error ? ? 9
Total ? ?
a. Complete the AOV table.
b. At the 0.01 level of significance, test to see whether there is any significant difference among means.

3. What are factorial designs? When are they used?

4. Draw the profile plot of a 2 × 3 factorial design when interactions are present.
5. The calculations for a factorial experiment involving three levels of factor A, four levels of factor B, and four replications resulted in the data below. 
SSTOT = 326; SSA = 78; SSB = 96; SSAB = 72
Set up an AOV tables and test for any significant main effects and any interaction effect. Level of significance alpha = 0.05.
6. A factorial experiment involving three levels of factor A and two levels of factor B resulted in the following data:
                    Factor B
            Level 1 Level 2
Level 1         50         48
                36         34
Factor A Level 2   49         67
                55         49
Level 3           87     59
                       93         44
a. Write an appropriate model for this experiment.
b. Set up an analysis of variance table and
i. test at the 5% level of significance to determine whether the factors A and B interact. 
ii. test at the 5% level of significance to determine whether differences exist among the levels of factor A.
iii. test at the 5% level of significance to determine whether differences exist among the levels of factor B.
7. A researcher is studying the effect of three different row spacings on the yields of four varieties of cotton. He randomly assigns each row-spacing / variety combination to six 50’ × 50’ plots. Within each plot he randomly selects 12 plants and weighs the cotton yield of the individual plants.
a. Is this an observations study or an experimental study?
b. What type of treatment structure is this?
c. What is or are the treatment factor or factors?
d. What are the experimental units?
e. What are the measurement units? 
StatisticsNull hypothesis, ho: there is no significant differnce in the average fill between three companies.Alternative hypothesis, h1: at least one of the mean fill between three companies differ significantly.Procedure for obtaining ANOVA in excel: Data -> Data Analysis -> one factor Anova...

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