Solve the following Problem:
In a study designed to determine patients acceptance of a new pain reliever, 100 physicians each selected a sample of 25 patients to participate in the study. Each patient, after trying the new pain reliever for a specified period of time, was asked whether it was preferable to the pain reliever used regularly in the past. The results of the study are shown below. We are interested in determining whether or not these data are compatible with the hypothesis that they are draw from a population that follows a binomial distribution using chi-square goodness-of-fit test.
Number of patients out of 25 Number of doctors Total number of patients preferring preferring new pain reliever reporting this number new pain reliever by doctor
0 5 0
1 6 6
2 8 16
3 10 30
4 10 40
5 15 75
6 17 102
7 10 70
8 10 80
9 9 81
10 or more 0 0
Total 100 500