# ANOVA problems

Please show all work for both problems.

1. Random samples of five were selected from each of three populations. The sum of squares total was 100. The sum of squares due to the treatments was 40.

a. Set up the null hypothesis and the alternate hypothesis.
b. What is the decision rule? Use the .05 significance level.
c. Complete the ANOVA table. What is the value of F?
d. What is your decision regarding the null hypothesis?

2. Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:

Summary
Groups Count Sum Average Variance
Line A 6 250 41.66667 0.266667
Line B 6 260 43.33333 0.666667
Line C 6 249 41.5 0.7

ANOVA
Source of Variation SS df MS F p-value
Between Groups 12.33333 2 6.166667 11.32653 0.001005
Within Groups 8.166667 15 0.544444
Total 20.5 17

a. Use a .01 level of significance to test if there is a difference in the mean production of the three assembly lines.
b. Develop a 99 percent confidence interval for the difference in the means between Line B and Line C.

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