Question

A company specializing in parachute assembly claims that its main parachute failure rate is at most 1%. You perform a hypothesis test to determine whether the company's claim is true or false. Your sample data resulted in enough evidence to go against the claim made by the company. It was later determined that the claim made by the company was actually incorrect. What kind of error, if any, was committed

Answer 1

There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.

Explanation:

A company specializing in parachute assembly claims that its main parachute failure rate is at most 1%.

At the null hypothesis, we test if the proportion is of at most 1%, that is:

`H_0: p \leq 0.01`

At the alternative hypothesis, we test if the proportion is of more than 1%, that is:

`H_0: p > 0.01`

Type I and type II errors:

Type I: Rejection of a true null hypothesis. The null hypothesis is true, but from a sample, you get enough evidence to reject.

Type II: Non-rejection of a false null hypothesis. The null hypothesis is false, but from a sample, you do not get enough evidence to reject.

Your sample data resulted in enough evidence to go against the claim made by the company.

This means that there was enough evidence to reject the null hypothesis.

It was later determined that the claim made by the company was actually incorrect.

The null hypothesis was false.

What kind of error, if any, was committed?

There was enough evidence to reject the null hypothesis, and in fact, the null hypothesis is false, which means that no error was committed.