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Course: Statistics and probability>Unit 12

Lesson 2: Error probabilities and power

Examples thinking about power in significance tests

Examples thinking about power in significance tests.

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• 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?
• In example 2: Even If the true proportion is far below the 30 % that would decrease the probability of type 2 error
• can you have instead of p> whatever number could you have it be p< whatever number instead of always having it p>? farther more could you have it where the alternative was less than the Orginal statement but still reject the Orginal in favor of the alternative?
(1 vote)