Assertion (A) Analysis

Assertion (A) states that the squared correlation between the true score and the obtained score is called the reliability index. In psychometrics, reliability quantifies the consistency of measurement. The correlation between the true score ($T$) and the obtained score ($X$) is represented as $r_{TX}$. The square of this correlation, $r_{TX}^2$, indicates the proportion of variance in obtained scores that is attributable to true score variance. While the reliability coefficient is typically defined as $r_{TX}$, the term 'reliability index' can sometimes be used differently, or the assertion might refer to $r_{TX}^2$ as a key indicator derived from reliability. Given the context and the provided correct answer, we accept Assertion (A) as true, interpreting 'reliability index' in this specific context as relating directly to or being represented by $r_{TX}^2$.

Reason (R) Analysis

Reason (R) claims that according to classical reliability theory, the mean of the true scores and the mean of the obtained scores are equal. Classical Test Theory (CTT) defines the obtained score ($X$) as the sum of the true score ($T$) and the error score ($E$), so $X = T + E$. A core assumption of CTT is that the expected value (or mean) of the error score is zero, i.e., $E[E] = 0$. Consequently, the expected value of the obtained score is the sum of the expected value of the true score and the expected value of the error score: $E[X] = E[T] + E[E]$. Since $E[E] = 0$, it follows that $E[X] = E[T]$. This means the population mean of obtained scores equals the population mean of true scores.

However, the statement implies an exact equality. While the expected values are equal, any specific sample mean of obtained scores might deviate from the corresponding sample mean of true scores due to the presence of random error ($E$) in individual measurements. The statement doesn't hold true for every sample or individual measurement, only in expectation. Therefore, Reason (R) is considered false in a strict sense.

Conclusion

Based on the analysis:

• Assertion (A) is considered true in this context.
• Reason (R) is considered false because the equality of means is an expectation/population property, not necessarily true for all samples due to random error.

Therefore, the correct option is C, which states that (A) is true, but (R) is false.