6. Suppose when getting ready for school you make the null hypothesis that it is

Question

6. Suppose when getting ready for school you make the null hypothesis that it is not going to rain. Identify which of the statements below give a type 1 and type 2 error in context and explain how you know. Then explain which error you would like to protect more strongly against making and how you would set your significance level for evaluating evidence against your null accordingly. (a) You take your umbrella to work but don't end up needing to use it because it never rains. (b) You leave your umbrella at home and get rained on walking between classes.

Explanation / Answer

We would first of all define the null and alternate hypothesis as shown below: -

H0: It will not rain

H1: It will rain

Type 1 error occurs when we reject a null hypothesis when it should have been retained. Type 2 error occurs when we incorrectly retain a false null hypothesis.

a)

Here, you take umbrella to work considering it would rain but it doesnt. This means, you considered that H1 to be true and H0 to be false and rejected H0 whereas it shouldnt have been rejected. Thus, this is a type 1 error.

b)

Here, you leave your umbrella at home and it rains. This means you considered H0 to be true but infact it is not. This is a case of type 2 error.

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