Question

Question 5

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.

Answer 1

Solution:

We are given

Null hypothesis: H0: Barb’s scuba gear is not safe.

Alternative hypothesis: Ha: Barb’s scuba gear is safe.

We know that the type I error occurred when we reject the null hypothesis when it is true. The type II error is occurred when we do not reject the null hypothesis when it is not true.

The type I error in the context of this problem is the error occurred when we conclude that Barb’s scuba gear is safe, however, in fact Barb’s scuba gear is not safe. In other words, the type I error is the probability of rejecting the null hypothesis that Barb’s scuba is not safe when it is not safe.

The type II error in the context of this problem is the error occurred when we conclude that Barb’s scuba gear is not safe, however, in fact Barb’s scuba gear is safe. In other words, the type II error is the probability of do not rejecting the null hypothesis that Barb’s scuba is not safe when it is safe.

The selection of the level of significance is depends on the fact how much significant results researcher wants for their study. Most of the time we select the level of significance as 5%, but if you want to perform your hypothesis more significantly then you can use 2% or 1% level of significance. The choice of selection of significance level is depends on how much you want to significant is your test.