The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set ? = 0.05. The test statistic for this hypothesis test would be .
A)$$z \bar { x }$$ = - 2.29
B)$$z \bar { x }$$= - 1.04
C)$$z \bar { x }$$= - 2.11
D)$$z \bar { x }$$ = 1.90

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula $$z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $$z = \frac{10.6 - 12}{(4.1/\sqrt{45})}$$ results in $z = -2.29$, which matches choice A.

The Department of Transportation Would Like to Test the Hypothesis zxˉz \bar { x }zxˉ

The Department of Transportation Would Like to Test the Hypothesis $z \bar { x }$