Question

Employers want to know which days of the week employees are absent in a five-day work week. Most employers would like to believe that employees are absent equally during the week. Suppose a random sample of 60 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in Table 11.6. For the population of employees, do the days for the highest number of absences occur with equal frequencies during a five-day work week? Test at a 5% significance level. Monday 15, Tuesday 12,Wednesday 9,Thursday9, Friday15, Number of Absences

Answer 1

Null Hypothesis H0: The absent day occur with equal frequencies.

Alternative Hypothesis H1: The absent days occur with unequal frequencies

Under H0, the rexpected frequencies are

E =(15+12+9+9+15)/5 =60/5 =12

The Calculations for Chi square test statistic is

Day	O	E	(O-E)^2/E
Monday	15	12	0.75
Tuesday	12	12	0
Wednesday	9	12	0.75
Thursday	9	12	0.75
Friday	15	12	0.75
Total	60	60	3

The test statistic is

Degrees of freedom = n-1=5-1= 4

Significance level

The critical value of Chi square for 4 df at 5% significance level is 9.488

The p value is 0.5578

Since p value is greater than significance level. Fail to Reject H0.

Hence, at 5 percent level of significance there is sufficient evidence to conclude that the absent days occur with equal frequencies.