Answer
a) The claim is supported.
b) The claim is supported.
c) The two departments have similar hit rates.
Work Step by Step
a) We want to see if the mean is different to $\frac{182}{540}=0.3370$, so we know $H_0:μ=0.3370$ and $H1:μ\ne0.3370$. We now use a Ti-84 calculator. To solve, go to "Stat," then "Tests," and then select "Stats." Doing this, we can find that the critical value and use a z-table calculator to find that $p\gt0.05$, hence the claim is valid.
b) We use a TI-84 calculator to find the confidence interval. To do this, we press “Stat” and then select “Tests.” Next, we select “2-PropZInt” to conduct the test. Doing this, we can find that the confidence interval goes through $0$, so the claim is valid.
c) The results show that the two police departments do have the same hit rates.
