over a 65 day period before speed cameras were introduced the average number of
ID: 3173242 • Letter: O
Question
over a 65 day period before speed cameras were introduced the average number of traffic accidents per day on a stretch of intersate was 7.25 with a standard deviation of 2.1. in the following 55 day period the average number of accidents was 7.08 with a standard deviation of 2.3
(i) are these means significantly different using a=0.05
(ii) what is the probability of making a type 1 error? that is how likely is it we would observe a difference in the means at least large IF the cameras made no difference in driving behaviour
Explanation / Answer
Given that,
population mean(u)=7.25
standard deviation, =2.3
sample mean, x =7.08
number (n)=55
null, Ho: =7.25
alternate, H1: !=7.25
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 7.08-7.25/(2.3/sqrt(55)
zo = -0.54815
| zo | = 0.54815
critical value
the value of |z | at los 5% is 1.96
we got |zo| =0.54815 & | z | = 1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -0.54815 ) = 0.58359
hence value of p0.05 < 0.58359, here we do not reject Ho
ANSWERS
---------------
null, Ho: =7.25
alternate, H1: !=7.25
test statistic: -0.54815
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.58359
are these means significantly different
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