7. A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. At the .01 significance level, is it reasonable to conclude that the modification reduced the number of traffic accidents?

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wifilethbridge wifilethbridge · Answer 1 · 2020-10-15T14:49:07+02:00

Answer:

Modification has not reduced the number of accidents.

Step-by-step explanation:

[tex]H_0: \mu\geq0\\H_a:\mu <0[/tex]

A B C D E F G H

Before modification 5 7 6 4 8 9 8 10

After modification 3 7 7 0 4 6 8 2

Difference -2 0 1 -4 -4 -3 0 -8

Mean of differences [tex]M_d = \frac{sum}{8}=\frac{2+0-1+4+4+3-0+8}{8}=2.5[/tex]

Standard deviation of differences = [tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n}}=2.9277[/tex]

Formula of paired t test :

[tex]t=\frac{M_d}{\frac{s}{\sqrt{n}}}\\t=\frac{2.5}{\frac{2.9277}{\sqrt{8}}}\\t = 2.4152[/tex]

Df = n-1 = 8-1 =7

[tex]t critical = t_{(df, \alpha)}=t_{7,0.01}=2.998[/tex]

t critical> t calculated

So, We failed to reject null hypothesis

Hence modification has not reduced the number of accidents.