need help for Stat question

Question

If sample data is such that for a one-tailed test of μ you can reject H₀ at the 1% level of significance, can you always reject H₀ for a two-tailed test at the same level of significance? Explain your answer.

a. No. The P-value for the two-tailed test could be greater than 0.01.

b.Yes. The P-value for the two-tailed test could be greater than 0.01.   

c. No. If H₀ for a one-tailed test is rejected at the 1% level of significance, it will never be rejected for a two-tailed test at the same level of significance.

d.Yes. If H₀ for a one-tailed test is rejected at the 1% level of significance, it will always be rejected for a two-tailed test at the same level of significance.

Answer 1

A one-tailed test at alpha=0.01 is equivalent to doing a two-tailed test at alpha=0.005. The value of the test statistic remains the same, but the "cut-off" value changes. Using the same alpha In the two-tailed test, you need to split the alpha in half, and allot 1/2 of alpha in each tail. so the correct answer is D.