In a repeated-measures study, we are interested in the difference scores between two conditions for the same subjects. The null hypothesis in this context typically states that there is no difference between the two conditions.
If the null hypothesis is true for a two-tailed test, this means that the average difference between the two conditions is zero. This indicates that any variation in the difference scores is due to random chance rather than a systematic effect.
Thus, if the null hypothesis is true, the population mean of the difference scores, denoted as [tex]\(\mu_D\)[/tex], should be 0. This is because the null hypothesis posits that there is no systematic difference between the conditions being compared.
Therefore, the correct value for the population mean of the difference scores ( [tex]\(\mu_D\)[/tex] ) when the null hypothesis is true for a two-tailed test is:
[tex]\[
\mu_D = 0
\][/tex]
Thus, the correct answer is:
[tex]\[
\mu_D = 0
\][/tex]
