Question

5. 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.

(b) You leave your umbrella at home and get rained on walking between classes

Answer 1

We have null hypothesis

Ho : It is not going to rain

Type I error : We commit a Type 1 error if we reject the null hypothesis when it is true.

Type 2 error : A Type 2 error happens if we fail to reject the null when it is not true.

Thus for Type I error we reject null, when we assume that it is going to rain so we carry the umbrella, but actually null is true that is it does not rain.

Hence (a) indicates Type I error

For Type II error, we do not reject null, that is we assume it is not going to rain and we do not carry the umbrella, but actually it rains/

Hence (b) indicates Type II error

In this case, we would like to protect the Type II error strongly, that is, we would want to reduce the type II error as we would want to reduce the probability (β) of getting wet if it rains when we have not carried the umbrella.

Thus we should choose a significance level such that β is low

That is we want the power of the hypothesis (1-β) to be high.