In: Statistics and Probability
Suppose the null hypothesis is: Barb’s scuba gear is not safe. What would the type I and II errors be in this situation? Further, what would be an appropriate choice for the level of significance? Explain your choice.
For specifying hypothesis we usually need more information for example you said barb's scuba gear is not safe...hypothesis is not specified like this. It always be specified in the terms of some characterstic.
Let's say you measure safety of the gear by how much time it can support someone underwater or let's say out of 100 , 90 % of the time it satisfied some safety test.
But let's say you are defining hypothesis like that
NULL HYPOTHESIS: Barb's scuba gear is not safe
Alternative should be : Barb's scuba gear is safe
Type 1 error - You reject null hypothesis when it is actually true. That means barb's scuba gear was not safe but you accepted that it is safe by doing this you have committed type -1 error.
Type 2 error- You accept null hypothesis when alternative is true. i.e barb's scuba was safe but you declare it to be unsafe.
Choice of level of significance
The significance level is the probability of rejecting the null hypothesis when it is true.Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.
so we will set significance level 1% usual practice is to set 5%,Reducing the alpha level from 0.05 to 0.01 reduces the chance of a false positive (called a Type I error) . So as in this case getting a false positive can be life threatning for barb so we try to lower the probability of type 1 error.