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Thinking about Test Hypothesis I came up with a question related to them.

When you make the test with a $90\%$ confidence interval, you have $10\%$ probability of committing a type I error. Analogously, for $99\%$, you have $1\%$ probability of committing a type I error.

I wondered the following: Making a $99\%$ confidence interval test, is equivalent to making two $90\%$ confidence interval tests and reject only the null hypothesis if both let you reject it?

callculus42
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Masclins
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1 Answers1

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If you make a $90\%$ confidence interval test, the probability to make a type I error is 10%. Then you repeat it. The probability to make a type I error is $10\%$ again. The probability to make a type I error in both of the tests is $10\% \cdot 10\%=1\%$.

The probability to make a type I error in one $99\%$ confidence interval test is $1\%$.

Therefore in both cases the probability to make a type I error is $1\%$.

callculus42
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    That's the information I presented. My question is if that implies they are equivalent – Masclins Jul 31 '15 at 08:26
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    Yes, that is what I presented. They are equivalent in the sense, that the probability making a type I error are in both cases equal ($1%$). – callculus42 Jul 31 '15 at 08:30