Question

You are interested in understanding how often young people, ages 16-25, have been stopped and questioned by the police.

- You asked a sample of 195 young people how many times they have been stopped and questioned by the police.

- The mean number of times young people have been stopped and questioned by the police is 1.11, with a variance of 12.99.

*Note: please show all work

Answer 1

Given that,
population mean(u)=1.11
standard deviation, σ =3.604
Assume,sample mean, x =1
number (n)=195
null, Ho: μ=1.11
alternate, H1: μ!=1.11
level of significance, α = 0.05
from standard normal table, two tailed z α/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 = 1-1.11/(3.604/sqrt(195)
zo = -0.426
| zo | = 0.426
critical value
the value of |z α| at los 5% is 1.96
we got |zo| =0.426 & | z α | = 1.96
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -0.426 ) = 0.67
hence value of p0.05 < 0.67, here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=1.11
alternate, H1: μ!=1.11
test statistic: -0.426
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.67
we do not have enough evidence to support the claim that population mean number of times young people have been stopped and questioned by the police is 1.11

answered by: anonymous