As an alternative to flextime many companies allow employees

As an alternative to flextime, many companies allow employees to do some of their work at home.
Individuals in a random sample of 300 workers were classified according to salary and number of workdays
per week spent at home.
                                                                   Workdays at Home Per Week
                                Salary Less than one       Atleast one,but not all     All at home
Under $25,000                      38                               16                                     14
$25,000 to $49,999                 54                              26                                    12
$50,000 to $74,999                 35                              22                                     9
Above $75,000                        33                              29                                     12

Do the data present suffcient evidence to indicate that salary is dependant on the number of workdays
spent at home? Test using alpha = 0.05. (The Chi-Square Test of Independence)

Solution

Doing an Expected Value Chart,      
      
36.26666667   21.08   10.65333333
49.06666667   28.52   14.41333333
35.2   20.46   10.34
39.46666667   22.94   11.59333333

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    6.446545846      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    4      
          
df =    6      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    12.59158724      

Thus, we FAIL TO REJECT THE NULL HYPOTHESIS.

the data DOES NOT present suffcient evidence to indicate that salary is dependent on the number of workdays spent at home.