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Chi-square Test of Goodness of Fit & Association

13. John Isaac, Inc., a designer and installer of industrial signs, employs 60 people. The company recorded the type of the most recent visit to a doctor by each employee. A national assessment conducted in 2008 found that 53 percent of all physician visits were to primary care physicians, 19 percent to medical specialists, 17 percent to surgical specialists and 11 percent to emergency departments. Test at the 0.01 significance level if Isaac employees differ significantly from the survey distribution. Here are their results:

Visit Type Number of Visits
Primary care 29
Medical specialist 11
Surgical specialist 16
Emergency 4
25. A survey by USA today investigated the public's attitude toward the federal deficit. Each sampled citizen was classified as to whether they felt the government should reduce the deficit, increase the deficit, or if they had no opinion. The sample result of the study by gender are reported below.
Gender reduce the deficit Increase the deficit no opinion
Male 244 194 68
Female 305 114 25
At the .05 significance level, is it reasonable to conclude that gender is independent of a person's position on the deficit?
27. The claims department at Wise Insurance Company believe that younger drivers have more accidents and, therefore, should be charged higher insurance rates. Investigating a sample of 1200 wise policyholders revealed the following breakdown on whether a claim had been filed in the last three years and the age of the policyholder. Is it reasonable to conclude that there is a relationship between the age of the policyholder and whether or not the person filed a claim? Use a .05 significance level.
Age group No claim Claim
16 up to 25 170 74
25 up to 40 240 58
40 up to 55 400 44
55 or older 190 24
Total 1000 200

Solution Summary

The solution provides step by step method for the calculation of chi square test for goodness of fit and association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.