Question

A group of researchers want to determine if incidents of drunk driving are equally likely to occur on different days of the week (f_e = 0.143). They collect data on drunk driving arrests and calculate frequencies for each day of the week. They collected data from 406 incidents overall. They observed the following frequencies: Sunday (24), Monday (59), Tuesday (46), Wednesday (37), Thursday (50), Friday (92), Saturday (98). Use a one-variable chi-square analysis (where α = .001) to determine if there are significant differences in drunk driving arrests by day of the week.

       1.      Identify the null hypothesis

     2.      List your degrees of freedom

       3.      List the expected frequency (raw number) for drunk driving arrests on Fridays

Answer 1

1)

null hypothesis: drunk driving arrests occur with uniform distribution by day of the week.

2)

degrees of freedom=categories-1=7-1 =6

3) expected frequency (raw number) for drunk driving arrests on Fridays =np=406/7=58

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
Sun	1/7	24	58.00	-4.46	19.931
Mon	1/7	59	58.00	0.13	0.017
Tue	1/7	46	58.00	-1.58	2.483
Wed	1/7	37	58.00	-2.76	7.603
Thu	1/7	50	58.00	-1.05	1.103
Fri	1/7	92	58.00	4.46	19.931
Sat	1/7	98	58.00	5.25	27.586
total	1.000	406	406		78.655

test statisitc -78.655

p value =0.0000

reject Ho