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# ANOVA and Nonparametic Problems

1) Do a larger proportion of college students than young children eat cereal? Researchers surveyed both age groups to find the answer. The results are shown in the table below.
(a) State the hypotheses used to answer the question.
(b) Using α = .05, state the decision rule and sketch it.
(c) Find the sample proportions and z statistic.
(d) Make a decision.
(e) Find the p-value and interpret it.
(f ) Is the normality assumption fulfilled? Explain.

College Students Young Children

Statistic (ages 18-25) (ages 6-11)
Number who eat cereal x1 = 833 x2 = 692
Number surveyed n1 = 850 n2 = 740

2) Has the cost to outsource a standard employee background check changed from 2005 to 2006? A random sample of 10 companies in spring 2005 showed a sample average of \$105 with a sample standard deviation equal to \$32. A random sample of 10 different companies in spring 2006 resulted in a sample average of \$75 with a sample standard deviation equal to \$45.
(a) Conduct a hypothesis test to test the difference in sample means with a level of significance equal to .05. Assume the population variances are not equal.
(b) Discuss why a paired sample design might have made more sense in this case.

3) A cognitive retraining clinic assists outpatient victims of head injury, anoxia, or other conditions that result in cognitive impairment. Each incoming patient is evaluated to establish an appropriate treatment program and estimated length of stay. To see if the evaluation teams are consistent, 12 randomly chosen patients are separately evaluated by two expert teams (A and B) as shown. At the .10 level of significance, are the evaluator teams consistent in their estimates? State your hypotheses and show all steps clearly.

Estimated Length of Stay in Weeks
Patient
Team 1 2 3 4 5 6 7 8 9 10 11 12
A 24 24 52 30 40 30 18 30 18 40 24 12
B 24 20 52 36 36 36 24 36 16 52 24 16

#### Solution Summary

The solution uses ANOVA and nonparametric parameters to determine if college students or young children eat more cereal.

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