LESSON 7: Analysis of Variance

For exercise problems 1 through 5, the following is a partially complete ANOVA table for a two-factor factorial experiment.

1. Give the number of levels for each factor.
2. How many observations were collected for each factor-level combination?

3. Complete the ANOVA table.

4. Test to determine whether the treatment means differ. Use \(\alpha =0.10\).

5. Test whether factors A and B interact using a = .10.

6. (a) Test whether there is a difference in the four means of factor A using a = .10.

b) Test whether there is a difference in the two means of factor B using a = .10.

#7) The steel ingot experiment. A quality control supervisor measures the quality of a steel ingot on a scale from 0 to 10. He designs an experiment in which three different temperatures (ranging from 1,100 to 1,200°F) and five different pressures (ranging from 500 to 600 psi) are utilized, with 20 ingots produced at each Temperature Pressure combination. Identify the following elements of the experiment:

1. Response
2. Factor(s) and factor type(s)
3. Treatments
4. Experimental units

#8) A partially completed ANOVA table for a completely

1. Complete the ANOVA table.
2. How many treatments are involved in the experiment?
3. Do the data provide sufficient evidence to indicate a difference among the population means? Test using a = .10.
4. Find the approximate observed significance level for the test in part c, and interpret it.
   #9) Consider a completely randomized design with 5 treatments, A. B. C, D, and E. The ANOVA F-test revealed significant differences among the means. A multiple comparisons procedure was used to compare all possible pairs of treatment means at a .05. The ranking of the 5 treatment means is summarized below. Identify which pairs of means are significantly different.
   
   #10) An experiment was conducted using a randomized lock design. The data from the experiment are displayed in the following table.
   
   1. Fill in the missing entries in the ANOVA table.
      
      b. Specify the null and alternative hypotheses you would use to investigate whether a difference exists among the treatment means.
      c. What test statistic should be used in conducting the test of part b?
      d. Describe the Type I and Type II errors associated with the hypothesis test of part (b)
5. Conduct the hypothesis test of part b using a = .05.

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