Question

three different traffic routes are tested for mean driving time. the entries in the table 13.18 are the driving times in minutes on the three different routes.
route 1
30
32
27
35
route 2
27
29
28
36
route 3
16
41
22
31
table 13.18
state ss_between.
o a. 26
o b. 200
o c. 250
o d. 35

Explanation:

Step1: Calculate the mean of each route

For Route 1: \(\bar{x}_{1}=\frac{30 + 32+27+35}{4}=\frac{124}{4} = 31\)
For Route 2: \(\bar{x}_{2}=\frac{27+29+28+36}{4}=\frac{120}{4}=30\)
For Route 3: \(\bar{x}_{3}=\frac{16 + 41+22+31}{4}=\frac{110}{4}=27.5\)

Step2: Calculate the grand mean

\(\bar{x}_{grand}=\frac{124 + 120+110}{12}=\frac{354}{12}=29.5\)

Step3: Calculate \(SS_{between}\)

\(SS_{between}=n_{1}(\bar{x}_{1}-\bar{x}_{grand})^{2}+n_{2}(\bar{x}_{2}-\bar{x}_{grand})^{2}+n_{3}(\bar{x}_{3}-\bar{x}_{grand})^{2}\)
\(n_{1}=n_{2}=n_{3} = 4\)
\(SS_{between}=4\times(31 - 29.5)^{2}+4\times(30 - 29.5)^{2}+4\times(27.5 - 29.5)^{2}\)
\(=4\times(2.25)+4\times(0.25)+4\times(4)\)
\(=9+1 + 16\)
\(=26\)

Answer:

A. 26