Final answer:
The statement is true; a paired t-test increases the power of the test for paired sample data by accounting for the natural pairing and reducing inter-sample variability.
Step-by-step explanation:
The statement is True. When sample data occur in pairs, using a paired t-test can indeed increase the power of the test as opposed to treating each sample independently. One reason for this is that the paired t-test reduces the variability within the samples by accounting for the natural pairing in the data, which in turn often leads to a more sensitive test capable of detecting a true effect.
In a hypothesis test for matched or paired samples, subjects are matched in pairs and differences between the paired observations are analyzed. The t-test for matched samples calculates the differences and then applies a Student’s t-test for a single population mean, using n - 1 degrees of freedom, where n is the number of pairs. This is more effective in handling the dependency between the pairs and can uncover effects that might be obscured when samples are treated as independent.
It is also important to note that using a larger sample size enhances the power of a test, according to the central limit theorem. Additionally, when sample sizes are small, which is often the case with matched samples, using a paired t-test can still provide sufficient power to detect an effect.