If the Type I error, α for a given test is to be decreased, then for a fixed sample size:
the Type II error (β) will also decrease.
the Type II error (β) will increase.
the power of the test will increase.
a one-tailed test must be utilized.
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The type 2 error will increase. This is the give and take with hypothesis tests. For a fixed sample number, you cannot reduce the size of one type of error without raising the other.