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.

the hypotheses are:

$h_0 : p = 0.12$

$h_1 : p < 0.12$

explain the meaning of a type i error.

\bigcirc concluding that the smog-level has increased when it actually has not.
\bigcirc not concluding that the smog-level has decreased when it actually has.
\bigcirc concluding that the smog-level has decreased when it actually has not.
\bigcirc not concluding that the smog-level has increased when it actually has.

Explanation:

A Type I error occurs when we reject the null hypothesis ($H_0$) when it is actually true. Here, $H_0: p = 0.12$ (smog - level is 12% pollutants) and $H_1: p<0.12$ (smog - level has decreased). So a Type I error would be concluding that the smog - level has decreased (rejecting $H_0$) when in reality it has not ( $H_0$ is true).

Answer:

C. Concluding that the smog - level has decreased when it actually has not.