The following is the result of sample survey regarding the employment of adult males and females.
Status sex
Male. Female
Employed. 160. 440
Not employed. 40. 360
Does this survey reveal any association between the sex of an individual and his or her employment? Use 5% level of significance
Yes, this survey reveals an association between the sex of an individual and his or her employment. To test this association, we can use a chi-square test of independence. The null hypothesis is that there is no association between the sex of an individual and his or her employment. The alternative hypothesis is that there is an association between the sex of an individual and his or her employment. The chi-square test statistic is calculated as follows:
Chi-square = (160-200)2/200 + (440-400)2/400 + (40-200)2/200 + (360-400)2/400 = 16.00
The critical value of chi-square at 5% level of significance is 7.81. Since the calculated value of chi-square (16.00) is greater than the critical value (7.81), we reject the null hypothesis and conclude that there is an association between the sex of an individual and his or her employment.