A company manager wishes to test a union leaders claim that

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 a = 0.05, where the following data have been compiled

Day

Sun

Mon

Tue

Wed

Thru

Absents

Solution

For the given question we apply the chi square test.

Ho: Absence occur during the days with same frequency

H1: Absence occure during the days with different frequency

Total absents during the week (five days) = 130

Expected absents per day = 26

Day                                     Sun               Mon             Tue              Wed            Thru

Observed frequency (Oi)              37                  15               12                23                43

Expected frequency (Ei)              26 26 26    26    26

Pobability (y)                               0.2                  0.2              0.2                0.2              0.2

testing is done using R software and code is given below;

x<-c(37,15,12,23,43)   # number of absents in day during the week
y<-rep(0.2,5)               # probability in the case of frequeny is same during the week
chisq.test(x,p=y)

Chi-squared test for given probabilities

data: x
X-squared = 28.3077, df = 4, p-value = 1.08e-05

in the question level of significance is 0.05 and calculated p- value is 1.08e-05 which is less than the 0.05 its means that Ho is rejected at 5 % level of significance. hence we say that absence occure during the days with different frequency.