Question

Suppose you want to test the claim that mean cost of textbooks for a stats class (offered by several different universities) is more than $150 at the \alpha ?=.05 significance level. (a) Explain, in the context of the problem, what it would mean to make a type I error. (b) Explain, in the context of the problem, what it would mean to make a type II error. (c) How does the the significance level relate to the type I and/or type II error?

Answer 1

Here, the problem is to test the claim that mean cost of textbooks is more than $150.

Hence, this can be considered as a testing problem between the null huypothesis aginst the alternative hypothesis .

Part (a)

In this context, type I error, i.e. rejecting a true null hypothesis will be deciding that the mean cost is more than $150, when it is actually less than or equal to $150.

Part (b)

In this context, type II error, i.e. accepting a false null hypothesis will be deciding that the mean cost is less than or equal to $150, when in reality, it is more than that.

Part (c)

The significance level acts as an upper bound of the probability of type I error, keeping in mind this constraint, type II error probability is minimised. Sp in this context, the test must be designed in such a way that the probability of the wrong decision that mean cost of textbooks is more than $150 when it is not the case is not more than .