Question

1)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 71 managers were asked on which day of the week they had the highest number of employee absences. The results were distributed as in Table. 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 0.05% significance level.

Day	Observed Frequency
Monday	10
Tuesday	13
Wednesday	19
Thursday	14
Friday	15

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places.)
χ2=χ2=

What are the degrees of freedom for this test?
d.f. =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

2)You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	X	Y	Z
A	20	17	38
B	26	50	47

Give all answers rounded to 3 places after the decimal point, if necessary.

(a) Enter the expected frequencies below:

	X	Y	Z
A
B

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=χ2=

(c) What is the critical value for this test of independence when using a significance level of αα = 0.10?
      Critical Value: χ2=

Answer 1

1)

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Monday	0.200	10	14.20	-1.11	1.242
Tuesday	0.200	13	14.20	-0.32	0.101
Wednesday	0.200	19	14.20	1.27	1.623
Thursday	0.200	14	14.20	-0.05	0.003
Friday	0.200	15	14.20	0.21	0.045
total	1.000	71	71		3.014

X² =3.014

d.f. = 4

p-value = 0.5555

2)

a)

Ei=row total*column total/grand total	X	Y	Z
A	17.424	25.379	32.197
B	28.576	41.621	52.803

b)
X² =6.750

c)

Critical Value: χ2=4.605