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Answer: P(Type I error) decreases | P(Type II error) increases
## Explanation ### Decreasing significance level from 5% to 1%: - **Type I error decreases** because significance level (α) = P(Type I error) - **Type II error increases** because reducing α makes the test more conservative, increasing the chance of failing to reject a false null hypothesis ### Reducing sample size from 1,000 to 500: - **Type II error increases** because smaller sample size reduces test power, making it harder to detect true effects - Type I error is not directly affected by sample size changes **Option B is correct** because: - Decreasing significance level: P(Type I error) decreases - Reducing sample size: P(Type II error) increases
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An oil industry analyst with a large international bank has constructed a sample of 1,000 individual firms on which she plans to perform statistical analyses. She considers either decreasing the level of significance used to test hypotheses from 5% to 1%, or removing 500 state-run firms from her sample. What impact will these changes have on the probability of making Type I and Type II errors?
A
P(Type I error) increases | P(Type I error) increases
B
P(Type I error) decreases | P(Type II error) increases
C
P(Type II error) increases | P(Type I error) decreases
D
P(Type II error) decreases | P(Type II error) decreases
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