Arrange the following events in order of decreasing likelihood of Type-I error:
1.Keeping significance level at 0.05 for a two-tailed test
2.Keeping significance level at 0.05 for a one-tailed test
3.Keeping significance level at 0.01 for a two-tailed test
4.Keeping significance level at 0.01 for a one-tailed test
A1, 2, 4, 3
B1, 4, 3, 2
C2, 1, 4, 3 ✓ Correct
D2, 4, 1, 3
Correct answer: (C) 2, 1, 4, 3
Explanation
Type-I error rises with the significance level and with a one-tailed critical region, so the order runs from one-tailed 0.05 down to two-tailed 0.01.
A one-tailed test at 0.05 has the smallest critical value and the greatest chance of a false rejection.
A two-tailed test at 0.05 splits the same 0.05 across both tails, needing a more extreme value.
A one-tailed test at 0.01 lowers the significance level and thus the Type-I risk further.
A two-tailed test at 0.01 is the most conservative, giving the least Type-I error.
Type-I error means rejecting a true null hypothesis, controlled directly by the chosen alpha.
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