Question

a national online business magazine reports that the average cost of a speeding ticket in miami, including court fees, is $220. a local police department claims that this amount has increased. to test their claim, they collect data from a simple random sample of 16 drivers who have been fined for speeding in the last year. assuming that the distribution of speeding ticket costs is normally distributed and the population standard deviation is $12, is there sufficient evidence to support the police departments claim at the 0.02 level of significance?
speeding ticket costs in miami
$225 $209 $234 $217 $226 $233 $240 $203
$233 $219 $220 $235 $229 $247 $213 $221
step 2 of 3: compute the value of the test statistic. round your answer to two decimal places.

Explanation:

Step1: Calculate sample mean

First, sum all the data values: $225 + 209+234 + 217+226+233+240+203+233+219+220+235+229+247+213+221 = 3554$. Then, divide by the sample size $n = 16$. The sample mean $\bar{x}=\frac{3554}{16}=222.125$.

Step2: Identify parameters

The population mean $\mu = 220$, the population standard - deviation $\sigma = 12$, and the sample size $n = 16$.

Step3: Calculate the test statistic

The formula for the z - test statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$. Substitute the values: $z=\frac{222.125 - 220}{\frac{12}{\sqrt{16}}}=\frac{2.125}{\frac{12}{4}}=\frac{2.125}{3}\approx0.71$.

Answer:

$0.71$