Question

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.

Answer 1

The required null and alternative hypotheses are
`H_0: p=0.84` and
`H_a: p<0.84` respectively.

Explanation:

Consider the provided information.

If there is no statistical significance in the test then it is know as the null which is denoted by
`H_0`, otherwise it is known as alternative hypothesis which denoted by
`H_a`.

The claim is: The proportion of crimes committed after dusk will fall below the current level of 0.84

The null hypothesis is The proportion of crimes committed after dusk will same as the current level of 0.84.

Therefore,

`H_0: p=0.84`

`H_a: p<0.84`

Hence, the required null and alternative hypotheses are
`H_0: p=0.84` and
`H_a: p<0.84` respectively.