Question

Employers particularly 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. That is, the average number of times an employee is absent is the same on Monday, Tuesday Wednesday, Thursday, or Friday. Suppose a sample of 20 absent days was taken and the days absent were distributed as follows:

	Monday	Tuesday	Wednesday	Thursday	Friday
Number of Absences	5	4	2	3	6

for the population of employees, do the absent days occur with equal frequencies during a five-day work-week? test at a 5% significance level.

A.Hypothesis:

B.Degrees of freedom:

C.Expected number:

D.Test statistic:

E.Approximate p-value (include a graph that shows the relative position of the sample outcome and shade the area corresponding to the p-value.)

F.Decision:

G.Conclusion:

Answer 1

a) H0:  The absent days occur with equal frequencies during a five-day work-week

H1:  The absent days occur with not equal frequencies during a five-day work-week

Let the los be alpha = 5%

b) Degrees of freedom = 5-1 = 4

c) Expected number = (5+4+2+3+6)/5 = 4

d) From the given data

	Observed	Expected
	Frequency	Freq Ei	(Oi-Ei)^2 /Ei
Monday	5	4	0.25
Tuesday	4	4	0
Wednesday	2	4	1
Thursday	3	4	0.25
Firday	6	4	1
Total:	20	20	2.5

Test statistic is 2.5

e) P-Value: 0.6446

f) Here p-value > alpha 0.05 so we accept H0

g) Thus we conclude that the absent days occur with equal frequencies during a five-day work-week