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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 10

Lesson 7: Potential errors when performing tests

# Examples thinking about power in significance tests

Examples thinking about power in significance tests.

## Want to join the conversation?

• At first, I thought that b was the answer. My reasoning was that the largest n was best, so n = 200 was good. Then I thought that since a Type II error needs a false Ho to occur (failing to reject Ho when it is actually false), I thought that a proportion of 32% would make Ho true. That would then make P(type II error) = 0. This would make the power greater so b was, therefore, my choice.

I now realize that my thinking was flawed because Ho is p=0.3, and it's false in all the options. The fact that p = 32% in b does not make Ho more true than in the other options (where the true p is farther from Ho). Therefore, the farthest true proportion from 0.3 increases the power, because there is less overlap between the pdf of Ho and the pdf of the true proportion.

This was really just to write out my thought process to better my understanding, but if it ends up helping someone, right on! :) • Would there have been other ways to choose the null and alternative hypotheses?   