Final answer:
The statement that adjacent residuals should be correlated with each other is false; residuals should be independent in a well-specified regression model. The independent residuals assumption helps ensure valid parameter estimates and statistical inferences.
Step-by-step explanation:
The statement “Adjacent residuals should be correlated with each other” is false. In regression analysis, we assume that the residuals, or errors, are independent of each other. This independence is a key component for the classical linear regression model. If adjacent residuals were correlated, it would indicate a violation of the independence assumption, and it could lead to inefficient estimates of the model parameters and invalid inference. For a properly specified model, residuals should show no auto-correlation; that is, they should not be correlated with each other.
Regarding the reference information, in a hypothesis test on matched or paired samples, it is true that two measurements are drawn from the same pair of individuals or objects and that two sample means are compared to each other (Answer choices b and c).
It is also correct that with larger sample sizes, the central limit theorem states that the sampling distribution of the means becomes approximately normal, which means the normality of the underlying distributions becomes less critical.
Lastly, the recorded paired data of statistics students' anxiety levels suggests a test of dependent means since the measurements are taken from the same subjects at different times.