Question

The Scottsdale fire department aims to respond to fire calls in 4 minutes or less on average. Historically, the population of response times is normally distributed with a standard deviation of 1 minute. A random sample of 18 fire calls showed a mean response time of 4 minutes 30 seconds. The department would like to know if the sample provides evidence that the mean response time goal is not being met. Which test should be used?

Answer 1

Answer: Right-tailed z-test.

Explanation:

• When population standard deviation (
  `\sigma`) is known , then we perform z-test.

• When Alternative hypothesis is right / left / two tailed we perform right / left / two tailed test respectively.

Let
`\mu` be the population mean of response times.

Given : The Scottsdale fire department aims to respond to fire calls in 4 minutes or less on average.

The department would like to know if the sample provides evidence that the mean response time goal is not being met

i.e. the appropriate set of hypothesis would be :

`H_0: \mu\leq4`

`H_a: \mu>4` (
`H_a` is opposite of
`H_0`)

The population of response times is normally distributed with a standard deviation of 1 minute.

i.e.
`\sigma=1`

Since alternative hypothesis (
`H_a`) is right-tailed and population standard deviation is known, so we should perform right-tailed z-test.