Question

A local police chief claims that 42%of all drug-related arrests are never prosecuted. A sample of 600arrests shows that 38% of the arrests were not prosecuted. Using this information, one officer wants to test the claim that the number of arrests that are never prosecuted is less than what the chief stated. Is there enough evidence at the 0.02 level to support the officer's claim?

Step 1 of 7:

State the null and alternative hypotheses.

Answer 1

Null Hypothesis H0: True proportion of drug-related arrests which are never prosecuted is 42%.

Alternative Hypothesis Ha : True proportion of drug-related arrests which are never prosecuted is less than 42%.

Standard error of proportion SE =

= 0.02015

Test statistic, z = ( - p) / SE = (0.38 - 0.42) / 0.02015 = -1.99

P-value = P(z < -1.99) =  0.0233

Since, p-value is greater than 0.02 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that the true proportion of drug-related arrests which are never prosecuted is less than 42%.