Question

three different traffic routes are tested for mean driving time. the entries in the table below are the driving times in minutes on the three different routes. use an ANOVA to test the hypothesis. Route 1: 30, 32, 27, 35 Route 2: 27, 29, 28, 36 Route 3: 16, 41, 22, 31 1) find the numerator degrees of freedom 2) find the denominator degrees of freedom 3) find SS factor 4) find ss total 5) find the F statistic

Answer 1

(1)

N = The total number of subjects = 3 X 4 = 12

k = number of groups = 3

The numerator degrees of freedom = k - 1 = 3 - 1 = 3

(2)

The denominator degrees of freedom = N - k = 12 - 3 = 9

(3)

Route	N	Mean	Std. Dev.
Route 1	n1 = 4	1=31	s1 = 3.3665
Route 2	n2 = 4	2=30	s2 = 4.0825
Route 3	n3 = 4	3=27.5	s3 = 10.9087
Total	n = 12	=29.5	s = 6.5157

SS Factor = SS_B is given by:

        = 26

(4)

SS_Total is given by:

Thus,

(5)

MS_B =26/2 = 13

MS_W = 440.9996/9 =49

F statistic= 13/49 = 0.2653

So,

Answer is:

0.2653