When evaluating a dependent-samples t-test using difference scores, what does the null hypothesis state about the population mean difference score?

If a researcher theoretically expects a treatment to change scores in a specific direction, their alternative hypothesis for a dependent-samples t-test should still simply assert that the population mean difference score is not equal to zero.

A clinical psychologist investigates whether a new mindfulness app reduces stress. She measures the stress levels of 25 participants both before and after they use the app for one month. Match each component of her dependent-samples $t$-test to its corresponding description or mathematical notation for this specific study.

A researcher is evaluating the impact of a stress-reduction seminar by measuring the same group's cortisol levels before and after the session. Arrange the steps in the correct logical sequence to establish the statistical framework and formulate the hypotheses for a dependent-samples $t$-test.

In a two-tailed dependent-samples $t$-test, what does the alternative hypothesis ($H_1$) assert about the means of the two conditions in the population?

Match each type of hypothesis for a dependent-samples $t$-test with the conceptual claim it makes about the population being studied.

A psychologist investigates whether a relaxation technique reduces systolic blood pressure. They measure $20$ participants before and after the technique, calculating difference scores as $D = \text{After} - \text{Before}$. Because the researcher theoretically expects blood pressure to decrease, they conduct a one-tailed dependent-samples $t$-test. The alternative hypothesis ($H_1$) must state that the population mean difference score ($\mu_0$) is _____.

A clinical psychologist measures the anxiety levels of $25$ patients before and after they undergo a mindfulness intervention. To determine if the intervention had an effect, she runs a dependent-samples $t$-test on the difference scores. Under the null hypothesis for this study, the psychologist assumes that the population mean difference score ($\mu_0$) is equal to $0$.

A sports psychologist measures athletes' reaction times before and after a new visual training program. If the psychologist has a strong theoretical justification to expect that the program will specifically decrease reaction times, they can choose to perform a(n) _____ test rather than a two-tailed test.

A researcher is planning a dependent-samples $t$-test to evaluate the effectiveness of a memory-training exercise by comparing participants' recall scores before and after training. Order the following steps to construct the logical framework of the hypotheses, moving from the baseline null assumption to its mathematical representation, and then to the alternative assumption and its mathematical representation.

Define the null and alternative hypotheses for a dependent-samples $t$-test. In your definition, include both the conceptual explanation of what each hypothesis states about the population means and the corresponding mathematical notation for the mean difference score ($\mu_0$).

Based on this scenario, decide whether the researcher should use a one-tailed or two-tailed alternative hypothesis for their dependent-samples $t$-test. Justify your decision using the principles of hypothesis testing for difference scores.

An educational psychologist is testing whether a new study technique improves test scores. They calculate difference scores for each student by subtracting the pre-test score from the post-test score. State the null hypothesis for this dependent-samples $t$-test using the appropriate mathematical notation for the population mean difference score.