Following Hurricane Katrina many law makers were worried tha

Following Hurricane Katrina, many law makers were worried that the intense devastation in New Orleans would lead to a surge in crime. In order to assess this possibility, a group of sociologists collected detailed police reports from a sample of 75 blocks in New Orleans in the months immediately following the hurricane. These data suggested that the average violent crime rate among blocks in the sample was 1156 with a standard deviation of 125. FBI data from the same time period suggested that the overall crime rate in Louisiana at the time was roughly 925. Given this information, please answer the following questions

1. Construct a one-tailed hypothesis comparing the New Orleans mean violent crime rate to that of all Louisiana. (5 points) 2. Using an = 0.01, test the null hypothesis. (10 points)

3. Interpret your results (5 points)

4. Based on your findings, would you recommend that the Louisiana Governor increase the size of the police force in New Orleans? (5 points)

Solution

Set Up Hypothesis
Null, H0: U=925
Alternate,Louisiana Governor increase the size of the police force H1: U>925
Test Statistic
Population Mean(U)=925
Sample X(Mean)=1156
Standard Deviation(S.D)=125
Number (n)=75
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1156-925/(125/Sqrt(74))
to =16.004
| to | =16.004
Critical Value
The Value of |t | with n-1 = 74 d.f is 2.378
We got |to| =16.004 & | t | =2.378
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 16.0041 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

We have evidence to support Louisiana Governor increase the size of the police force