Question

1. The local sheriff of Floyden County started a “crimeline” program some years ago and wonders if it’s really working. The program publicizes unsolved violent crimes that occur in the county in the local media and offers cash rewards for information leading to arrests. Can the sheriff conclude that “featured” crimes more likely to be cleared by arrest than other violent crimes? Results from random samples of both featured and non-featured crimes that occurred in the county are reported below .

Sample 1: Crimeline Featured Crimes Cleared by Arrest	Sample 2: Non-Crimeline Crimes Cleared by Arrest
P1 = 0.45	P2 = 0.35
N1 = 171	N2 = 219

Answer 1

Answer)

Null hypothesis Ho : P1 = P2

Alternate hypothesis Ha : P1 > P2

First we need to check the conditions of normality that is if n1*p1 and n2*p2 both are greater than 5 or not

N1*p1 = 76.95

N2*p2 = 76.65

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (P1-P2)/standard error

Standard error = √{P*(1-P)}*√{(1/n1)+(1/n2)}

P = combined proportion = {(p1*n1)+(p2*n2)}/{n1+n2}

Z = 2.01

From z table,P(Z>2.01) = 0.0222

As the obtained P-value is small

We reject the null hypothesis

And we have enough evidence to conclude that featured” crimes more likely to be cleared by arrest than other violent crimes