Question

The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph. After a school speed limit sign of 20 mph is placed at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 alpha level, was there a significant change in driving speed?figure the effect size

Answer 1

First, we have to define the system of hypothesis

`\begin{gathered} H_0\colon\mu=35 \\ H_a\colon\mu\\e35 \end{gathered}`

Then, we find the statistic test value

`\frac{\sqrt[]{n}\cdot(\bar{x}-\mu)}{\sigma}`

It's important to know that this situation models a standard normal distribution.

Replacing the given information, we have

`\frac{\sqrt[]{40}\cdot|32-35|}{7.5}=\frac{|-3|\cdot\sqrt[]{40}}{7.5}=2.5`

This value allows us to deduct that the null hypothesis can't be rejected because the test statistic is not greater than 2.57583, it's equal. It's important to consider that this value refers to 0.5% of the distribution (two tales).

Hence, there's no significant evidence to reject the null hypothesis.