Question

Suppose you were considering going bungee jumping, but would only go if the mean breaking strength of the cord was greater than 250 pounds. If the mean breaking strength of the cord is greater than 250 pounds, the bungee cord will not break. What would be the Type II error for this problem?

Answer 1

Type II error will occur when we conclude that the mean breaking strength of the cord is smaller than or equal to 250 pounds but in actual it was not true.

Explanation:

We are given that you are considering going bungee jumping, but would only go if the mean breaking strength of the cord was greater than 250 pounds.

If the mean breaking strength of the cord is greater than 250 pounds, the bungee cord will not break.

Let
`\mu` = mean breaking strength of the cord

So, Null Hypothesis,
`H_0` :
`\mu \leq` 250 pounds

Alternate Hypothesis,
`H_A` :
`\mu` > 250 pounds

Here, null hypothesis states that the mean breaking strength of the cord was smaller than or equal to 250 pounds.

On the other hand, alternate hypothesis states that the mean breaking strength of the cord was greater than 250 pounds.

Now, Type II error states the Probability of accepting null hypothesis given the fact that it was false or Probability of accepting the false hypothesis.

SO, according to our question, Type II error will occur when we conclude that the mean breaking strength of the cord is smaller than or equal to 250 pounds but in actual it was not true and he mean breaking strength of the cord was greater than 250 pounds.