Suppose when getting ready for school you make the null hypothesis that it is no

Question

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

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is incorrectly retaining a false null hypothesis (also known as a "false negative" finding).

Here hypothesis is H_0:It will rain vs H_1: It will not rain

a. This is Type II error as you accepted that it will rain and took umbrella but it didn't rain

b. This is Type I error as you rejected the null hypothesis and didn't took umbrella

Type I error is to be protected as carrying a umbrella will not harm but not carrying and getting wet can make you ill

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