Answer to Question #226746 in Statistics and Probability for aoi

Question

Chi-Square Testing 

300 employees of a company were selected at random and asked whether they were in favour of a scheme to introduce flexible working hours. The following table shows the opinion and the departments of the employees.

              OPINION          

Department In favour Uncertain Against

Production 89 42 9

Sales 53 36 11

Administration 38 12 10

 

Test whether there is evidence of a significant association between opinion and department.

Answer 1

$H_0:$ Opinion on flexible working hours and department are independent

$H_a:$ Opinion on flexible working hours and department are dependent

$\chi^2=\sum_{\forall ij}\frac{(Oij-Eij)^2}{Eij}$

$Eij=\frac{row total(ith)\times Column total (jth)}{N}$

The table below shows the computations of Eij and chi-square

$\chi^2=\sum_{\forall ij}\frac{(Oij-Eij)^2}{Eij}$

$=0.2976+0+1.7857+0.81667+1.2+0.1+0.1111+2+2.6667$

$=8.97778$

Let $\alpha=0.05$

$df=(n-1)\times(m-1)$

$=(3-1)\times(3-1)$

$=4$

$CV=\chi^2_{4,0.05}=9.49$

$P-value=p(>9.97778)=0.06166$

Since the test statistic 8.97778 is less than the critical value 9.49, we fail to reject the null hypothesis. Similarly, since the p- value 0.06166 is greater than 0.05, we fail to reject the null hypothesis. Opinion on flexible working hours are independent of department. There is no association between opinion and department.