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# ANOVA & Confidence Interval

One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds, with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to a warmer climate where food is easily available. Birds with bigger brains on the other hand are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar the actual research results. The numbers represent relative brain size for the individual birds in each sample.

Non Migrating Short Distance Migrants Long distance migrant
18 6 4
13 11 9
19 7 5
12 9 6
16 8 5 12 13 7

M = 15 M= 9 M= 6
T= 90 T=54 T=36
SS= 48 SS=34 SS=16

a. Use an AVONA with a= .05 to determine whether there are any significant mean differences among the three groups of birds.
b. Compare n2, the percentage of variance explained by the group differences, for these data.
c. Use the Tukey HSD post test to determine which group is significantly different.

Problem 15 in chapter 10 described a study by Laughlin, Zander, Knieval, and Tan (2003) showing that groups of three people consistently outperformed the best of the individuals working alone on a letter to number substitution problem. the following data describe the number of trails needed of solve each problem for a sample of n= 15 groups and a sample of n= 15 individuals.

Groups individuals
n= 15 n=
M=3.8 M=4.7
SS= 15.4 SS= 18.2

a. Make a point estimate of how much better groups perform than individuals for the general population (Estimate the mean difference in the number of trails needed for a solution).
b. Make an interval estimate of the mean difference so that you are 95% confidence that the true mean differences is in your interval.
c. Based on your answer to part b, what would be the decision for a hypothesis test evaluating the significance of the mean difference using a two tailed test with a= .05. Explain your answer.

#### Solution Preview

Week 9
One possible explanation for why some birds migrate and other maintain year round residency in a single location is intelligence. Specifically, birds, with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to a warmer climate where food is easily available. Birds with bigger brains, on the other hand are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar the actual research results. The numbers represent relative brain size for the individual birds in each sample.

Non Migrating Short Distance Migrants Long distance migrant
18 6 4
13 11 9
19 7 5
12 9 6
16 8 5 12 13 ...

#### Solution Summary

This solution gives the step by step method for ANOVA and confidence interval. Formula for the calculation and Interpretations of the results are also included.

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