Final answer:
The statement is false because a two-tailed test checks for significance in both directions whereas a one-tailed test only assesses one direction. In a two-tailed test with alpha = 0.01, p-values below 0.005 or above 0.995 indicate rejection of the null hypothesis, which might not be the same direction assessed by a one-tailed test.
Step-by-step explanation:
The statement "A rejection in a two-tailed hypothesis test implies rejection in a one-tailed hypothesis test" is false. A two-tailed test evaluates the possibility of an effect in two directions, both higher and lower than a central value.
On the other hand, a one-tailed test only assesses the possibility of an effect in one direction, which could either be higher or lower. It's possible for a result to be significant in a two-tailed test but not in one direction of a one-tailed test if all the significant difference occurs in the opposite direction.
For example, if you conducted an independent-samples t-test with a sample size of 10 in each group and you set your significance level (alpha) to 0.01 for a two-tailed test, you would reject the null hypothesis if your p-value was less than 0.005 (because the tails are 0.005 each, adding up to 0.01) or greater than 0.995.
But in a one-tailed test with the same alpha level of 0.01, you would reject the null hypothesis only if the p-value was less than 0.01 (for a lower tail test) or greater than 0.99 (for an upper tail test).