Question

# 1)Employers want to know which days of the week employees are absent in a five-day work...

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=

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

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