Question

In: Statistics and Probability

Researchers have long suspected that texting has a detrimental effect on driving behavior. To avoid unnecessary...

Researchers have long suspected that texting has a detrimental effect on driving behavior. To avoid unnecessary high risk of driving on the roads, driving behavior is measured via driving simulator and the number of mistakes is recorded while texting and not texting as the person is driving the simulator. Mistakes such as failing to stay within the lane, driving at least 10 miles below or above the speed limit, and failing to use the turn signal are automatically recorded. To avoid individual differences in driving behavior, participants are tested twice: once under the “texting while driving” condition and once under the “driving without texting” condition. There are nine participants in the study. Their driving mistakes are reported in the table below.

Question: Do the data support the claim that texting has a detrimental (negative) effect on driving behavior, using an α = 0.05?

For this question, you must follow the steps of hypothesis testing and complete all your calculations by hand. Remember to show your calculations and provide your conclusions in sentence format.

Once you finish this part of the assignment, you can scan or take a photo of your work and paste the scan/photo in your Word document.

Table 1.

Number of mistakes by study participants while using the driving simulator

Participant

Texting

Not texting

A

35

21

B

48

30

C

25

10

D

33

10

E

30

11

F

46

22

G

37

16

H

33

10

I

37

23

Solutions

Expert Solution

Given that,
mean(x)=36
standard deviation , s.d1=7.2629
number(n1)=9
y(mean)=17
standard deviation, s.d2 =7.3314
number(n2)=9
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.306
since our test is two-tailed
reject Ho, if to < -2.306 OR if to > 2.306
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =36-17/sqrt((52.74972/9)+(53.74943/9))
to =5.5233
| to | =5.5233
critical value
the value of |t α| with min (n1-1, n2-1) i.e 8 d.f is 2.306
we got |to| = 5.52334 & | t α | = 2.306
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 5.5233 ) = 0.001
hence value of p0.05 > 0.001,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 5.5233
critical value: -2.306 , 2.306
decision: reject Ho
p-value: 0.001
we have enough evidence to support the claim that texting has a detrimental (negative) effect on driving behavior.


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