Question

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled.

Day	Mon	Tues	Wed	Thurs	Fri
Absences	37	15	12	23	43

Answer 1

= proportion of total absence on weekdays occurring on Monday.
= proportion of total absence on weekdays occurring on Tuesday.
= proportion of total absence on weekdays occurring on Wednesday.
= proportion of total absence on weekdays occurring on Thursday.
= proportion of total absence on weekdays occurring on Friday.

To test, versus the value of at least one of the is different from .

Now, observed frequencies = = (37, 15, 12, 23, 43). Total frequency = = 37+15+12+23+43 = 130.
Now, expected frequencies = = (130 * 0.2, 130 * 0.2, 130 * 0.2, 130 * 0.2, 130 * 0.2) = (26, 26, 26, 26, 26).

Test statistic =   =   = 28.30769.

Now, k = 5 = no. of weekdays. Critical value = .

Since, the test statistic is greater than the critical value, we reject . We conclude that there is enough evidence to reject the claim that absences occur on different week days with the same frequencies.