Question

Frank likes to do rock climbing and it is important that his equipment be in good condition. Suppose the null hypothesis is H0: Frank’s rock climbing equipment is safe.
-What is a type one error (false positive)?
-What is a type two error (false negative)?
-In this setting, which is worse?

Answer 1

Hello Sir/ Mam

Given that :

H0: Frank’s rock climbing equipment is safe.

(a) Type 1 error means rejection of true null hypothesis, also known as false positive.

In this case, type one error will mean that the null is true and still rejected, which means that Frank's rock climbing equipment is safe but deduced by the tests that the equipment is not safe.

(b) Type II error means failing to reject a false null, also known as false negative.

In this case, type two error will mean that null was false, but we still failed to reject it which means that Frank's equipment is not safe and we failed to deduce that it is un-safe.

(c) Type two error is more worse and fatal for Frank in this scenario.

As the consequences :

• Type one error : That a safe equipment is not used for the purpose of rock climbing.
• Type two error : That Frank will go on to climbing with an unsafe equipment and it can cost him his life.

I hope this solves your doubt.

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