Question

4 (15) A random sample of 100 student absences yielded the following data on the days of the week of which the absences occurred: Monday Tuesday Wednesday Thursday Friday 19 13 Day Observed Frequency 27 26 15 Test the hypothesis that an absence is equally likely to oceur on any of the five days. What lusions? Use the 5 percent level of significance. is

Answer 1

Null hypothesis: Ho:Absence occurs with uniform distribution over all five days

Alternate hypothesis: Ha:Absence does not occurs with uniform distribution over all five days

degree of freedom =categories-1=

4

for 4 df and 0.05 level of signifcance critical region       χ2=

9.488

applying chi square goodness of fit 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	27	20.00	1.57	2.450
Tuesday	0.200	19	20.00	-0.22	0.050
Wednesday	0.200	13	20.00	-1.57	2.450
Thursday	0.200	15	20.00	-1.12	1.250
Friday	0.200	26	20.00	1.34	1.800
total	1.000	100	100		8.000

as test statistic X² =8.00 does not fall in rejection region ; we can not reject null hypothesis.

We do not have evidence at 0.05 level to conclude that Absence does not occurs with uniform distribution over all five days