The Federal Bureau of Investigation (FBI) compiles information on robbery and pr

Question

The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was $468 in 2012. For last year, 12 randomly selected purse-snatching offenses yielded the following values lost, to the nearest dollar. a. Use a t-test to decide, at the 5% significance level, whether last year's mean value lost to purse snatching has decreased from the 2012 mean. The mean and standard deviation of the data are $455.0 and $86.8, respectively.

Explanation / Answer

Given that,
population mean(u)=468
sample mean, x =455
standard deviation, s =86.8
number (n)=12
null, Ho: =468
alternate, H1: <468
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.796
since our test is left-tailed
reject Ho, if to < -1.796
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =455-468/(86.8/sqrt(12))
to =-0.519
| to | =0.519
critical value
the value of |t | with n-1 = 11 d.f is 1.796
we got |to| =0.519 & | t | =1.796
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -0.5188 ) = 0.30708
hence value of p0.05 < 0.30708,here we do not reject Ho

ANSWERS
---------------
null, Ho: =468
alternate, H1: <468
test statistic: -0.519
critical value: -1.796
decision: do not reject Ho
p-value: 0.30708

we don't have evidence to support last year's mean value lost to pursue snatching is decreased

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