appropriate null and the alternative hypothesis

Problem 1

1. present a contingency table
   
   
2. state the appropriate null and the alternative hypothesis
   
   
3. for each test
   
   
   1. determine a critical value using
      
      
   2. present a test statistic
      
      
   3. present a p-value
      
      
   4. interpret  the p-value
      
      
   5. state your decision
      
      
   6. state your conclusion
      
      
      
      
      In a study of risk factors for allergic disease among 13 and 14 year old school children, one risk factor was a family history of eating an unbalanced diet. In the study, 656 of 2107 children who had an unbalanced diet exhibited symptoms of rhinitis, whereas 677 of 2339 children who had a balanced diet exhibited symptoms of rhinitis. 

1. 1. Perform the Z test to determine if there is a significant difference in the proportion of children with symptoms of rhinitis between those on an unbalanced diet and those on a balanced diet. 
   2. Perform the chi-square test to determine if there is a significant difference in the proportion of children with symptoms of rhinitis between those on an unbalanced diet and those on a balanced diet.
   3. Demonstrate the equivalence of the tests in a. and b.
   4. Use a 95 % confidence interval to estimate the difference in the proportion of children with symptoms of rhinitis between those on an unbalanced diet and those on a balanced diet.
   5. Provide an interpretation of your interval.
   6. Demonstrate how the confidence interval can also be used to test the hypothesis.

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