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_within.
o a. 441
o b. 400
o c. 351
o d. 205

Question

Accepted Answer

# Explanation:
## Step1: Calculate the mean for 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 $SS_{within}$
$$
\begin{align*}
SS_{within}&=\sum_{i = 1}^{n_{1}}(x_{i1}-\bar{x}_{1})^{2}+\sum_{i = 1}^{n_{2}}(x_{i2}-\bar{x}_{2})^{2}+\sum_{i = 1}^{n_{3}}(x_{i3}-\bar{x}_{3})^{2}\
&=(30 - 31)^{2}+(32-31)^{2}+(27 - 31)^{2}+(35-31)^{2}+(27-30)^{2}+(29 - 30)^{2}+(28-30)^{2}+(36-30)^{2}+(16-27.5)^{2}+(41-27.5)^{2}+(22-27.5)^{2}+(31-27.5)^{2}\
&=(- 1)^{2}+1^{2}+(-4)^{2}+4^{2}+(-3)^{2}+(-1)^{2}+(-2)^{2}+6^{2}+(-11.5)^{2}+13.5^{2}+(-5.5)^{2}+3.5^{2}\
&=1 + 1+16+16+9+1+4+36+132.25+182.25+30.25+12.25\
&=441
\end{align*}
$$

# Answer:
A. 441

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean for each route

Step2: Calculate \(SS_{within}\)

Answer: