The average age of licensed drivers in a county is = 42.6, = 12, and the distrib

Question

The average age of licensed drivers in a county is = 42.6, = 12, and the distribution is approximately normal. A county police officer was interested in whether the average age of drivers receiving parking tickets differed from the average age of the driving population. She obtained a sample of N = 25 drivers receiving parking tickets. The average age of these drivers was M = 40.5. Perform the six steps of hypothesis testing necessary to determine whether this group differs from the population of drivers in the county.

Explanation / Answer

Given that,
population mean(u)=42.6
standard deviation, =12
sample mean, x =40.5
number (n)=25
null, Ho: =42.6
alternate, group differs from the population of drivers in the county, H1: !=42.6
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 40.5-42.6/(12/sqrt(25)
zo = -0.875
| zo | = 0.875
critical value
the value of |z | at los 10% is 1.645
we got |zo| =0.875 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -0.875 ) = 0.38157
hence value of p0.1 < 0.38157, here we do not reject Ho
ANSWERS
---------------
null, Ho: =42.6
alternate, H1: !=42.6
test statistic: -0.875
critical value: -1.645 , 1.645
decision: do not reject Ho
p-value: 0.38157

We don't have evidence that group differs from the population of drivers in the county

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