According to the national survey, the rating of the service provided by American business is as indicated in Table 1 below. The question of the survey was; "In general, how would you rate the service that American businesses provide?"
Table 1: A national survey response of U.S customers on the quality of service
| Response | Excellent | Pretty good | Only fair | Poor |
| percentage | 8% | 47% | 34% | 11% |
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A store manager made observations to determine whether the result of the national survey applies to customers in his city. As such, the result of his observations on 207 customers, are as indicated in table 2. The observations, however, can be used to calculate the approximate chi-square distribution X 2 that is crucial for the chi-squared goodness-of-fit test. The null hypothesis is: the results of the national customer survey apply to customers of the supermarkets in the manager’s city. At a significance level of 0.05, the calculation of the approximate chi-squared distribution will be as follows.
Table 2: A manager’s observation on the quality of service for supermarket customers in a city
| Response | Excellent | Pretty good | Only fair | Poor |
| Observations | 21 | 109 | 62 | 15 |
| Expected observations | 16.56 | 97.29 | 70.38 | 22.77 |
X 2 =
X 2 =
X 2 = 1.190435 + 1.409437 + 0.997789 + 2.651423 = 6.249084
X 2 = 6.25 (the calculated chi-statistic)
From the given dataset, the degree of freedom is the total sample minus one. It gives a degree of freedom of 3. The critical value at a significance level of 0.05 is 7.82. It is more than the calculated value of 6.25. Hence, we conclude that the survey applies to the customers of the supermarket in the manager's city at a 0.05 significance level. The calculated value is equal to the critical value at a significance level of 0.10. The null hypothesis is also acceptable. However, at a significance level of 0.20, we reject the null hypothesis because the critical value is 4.64, which is more extreme than our calculated value of 6.25.
Application of a Chi-Squared Goodness-Of-Fit Test Application in the Human Resources Department for a Company
The chi-squared goodness-of –fit test is applicable in relating the relevance of research data to the observation within the human resource department. For instance, the human resource department may seek to establish whether the result of a just-concluded national survey applies to the industry. The survey sought to establish the relationship of employee performance to the salaries they receive within the sector. As such, managers within the department can choose to observe a sample of the employees and subject the data to the chi-squared goodness-of-fit test. The acceptance or rejection of the null hypothesis gives a general indication of the applicability of the national survey results on the firms within the industry.
