Question

After lowering the landing gear, the pilot notices that the "gear down and locked" light is not illuminated. "It's probably just a burned out light bulb," she says, as she proceeds on final approach for landing. Considering the pilot's hypothesis, which is the result of Type I error? Explain your choice!

A. The sound of metal scraping on concrete will be heard upon landing.

B. The landing is delayed unnecessarily while the bulb and gear are checked.

C. We cannot be sure without knowing whether or not the bulb is actually faulty.

When constructing and implementing hypothesis tests, what reasoning is
used behind the statement of the null and alternative hypotheses? Why
are hypothesis tests set up in this way?

Answer 1

Correct option:

B. The landing is delayed unnecessarily while the bulb and gear are checked.

Explanation:

H0: Null Hypothesis: The "gear down and locked" light is not illuminated. because "It's probably just a burned out light bulb,"

HA: Alternative Hypothesis: The "gear down and locked" light is not illuminated. because it is not just a burned out light bulb, but some other major problem.

The reasoning that is used behind the statement of the null and alternative hypotheses is as follows:

The null hypothesis proposes that there is no difference between certain characteristics of the population. In this situation, the null hypothesis is that there is no major problem - "It's probably just a burned out light bulb," The Alternative hypothesis is that it is not just a burned out light bulb, but some other major problem.

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, the "gear down and locked" light is not illuminated. because "It's probably just a burned out light bulb," But we wrongly conclude that the "gear down and locked" light is not illuminated. because it is not just a burned out light bulb, but some other major problem. Type I Error is committed inthissituation.

The consequence of Type I Error is that the landing is delayed unnecessarily while the bulb and gear are checked. because in reality "It's probably just a burned out light bulb.