Question

Perform the indicated goodness-of-fit test. 33) 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 the 0.05 level of significance if the following sample data have been compiled.

Day Mon Tue Wed Thur Fri

Absences 37 15 12 23 43

Please show how to calculate this answer on ti-83

Answer 1

It is expected that frequency of absences is same for each of five days (Monday to Friday)

total number of days = 5, so proportion p = (a single day)/(total days) = 1/5 = 0.2

Total frequency = 37+15+12+23+43 = 130

Expected frequency = total frequency*proportion = 130*0.2 = 26

Hypotheses are

Ho:- Observed distribution is same as Expected distribution

H1:- Observed distribution is different from Expected distribution

Using TI 83 calculator

Press STAT then EDIT and enter observed frequencies (37,15,12,23,43) in L1 and expected frequencies (26,26,26,26,26) in L2

Again

Press STAT then TESTS and select GOF Test

Observed = L1

Expected = L2

df = 4 (this is because df= number of categories-1 = 5-1 = 4 )

Press CALCULATE

we get

Test statistic = 28.308

p value = 0.0000

We have p value less than significance level, i.e. 0.0000 < 0.05, so we will reject the null hypothesis

Conclusion:- We have insufficient evidence to support the claim that the absences occur on the different week days with the same frequencies.