Question

For the given significance test, explain the meaning of a Type I error.

A metropolitan city is trying to bring its smog level into federal guidelines and currently has 12% pollutants per 10,000 volume of air. The city comes up with a new policy where city employees are encouraged to use city transportation to and from work. An independent agency, hired by the city, runs a test on the air in order to determine if the new policy has had the desired effect.
Explain the meaning of a Type I error.

Answer 1

A Type I error in this scenario would occur if the independent agency incorrectly concluded that the city's new policy has successfully reduced the smog level, when in fact there has been no significant change.

Step-by-step explanation:

In the context of hypothesis testing, a Type I error occurs when a true null hypothesis is incorrectly rejected. Let's apply this to the example provided. If the independent agency concludes that the city's new policy has significantly reduced the smog level (pollutants per 10,000 volume of air) below the current 12%, but in reality, the smog level has not changed, a Type I error has been made. In other words, the agency mistakenly believes the policy was effective when it was not. The consequences of a Type I error in this scenario could mislead policy-makers into thinking their efforts have been successful, potentially halting further action that may be needed to reduce pollution.