# What is the test statistic used for the anova procedure?

1. What is the test statistic used for the ANOVA procedure? Explain how it is calculated.

2. Suppose a researcher collected data to compare whether cats of different size categories differed in mean number of hours slept per day. Cats were categorized as small, medium, or large. The calculated F-statistic was 220.41.

A. Given this test statistic, can we conclude that there is more variation between groups or within groups?

B. Based on the test statistic, is it likely that an association exists between cat size and mean number of hours that a cat sleeps per day? Explain.

Researchers want to test whether the color of a vehicle ticketed for speeding has an effect on the amount of the ticket. Four vehicle colors were used for the study—red, white, black, and silver. Thirty vehicles were randomly assigned to each group. Use the output below to answer questions 3 and 4.

*One-way ANOVA *

*Variation between groups=2063.33 *

*Variation within groups=196.25 *

*p=4.5985705 x 10-4 *

3. Show how the F-statistics is calculated. Round to the nearest hundredth.

5. Write the correct decision regarding the null hypotheses and conclusion for the hypothesis that vehicle color affects the amount of a speeding ticket. Assume all ANOVA test conditions have been satisfied.

6. A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 10 employees with each of the three levels of training (Beginner, Intermediate and Advanced). Do the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training? The data is summarized in the table. Use this information for problems 5 – 9 and 11 question.

7. Assume the conditions for ANOVA have been met. Write out the null and alternate hypotheses using appropriate symbols.

6. Using a statistical computing program such as SPSS, Minitab, or StatCrunch, carry out the ANOVA test. Copy and paste the output.

7. Show how the test statistic is calculated from the output.

8. Specify the p-value and interpret its value.

9. Make the decision in terms of the null hypothesis. Write the conclusion in context of the data.

10. What happens if you try ANOVA with only two groups? Explain.

11. If the means are found to differ, which pairs of means differ? SHOW WORK

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