Final answer:
It is true that a single MSE value is not very informative on its own; it must be compared to other MSEs or industry benchmarks for meaningful insights. In hypothesis testing with paired samples, two measurements are drawn from the same individuals or objects, and two means are compared. Comparisons and considering the context are crucial for understanding statistical results.
Step-by-step explanation:
The statement that a single MSE calculation doesn't give us a whole lot of information and that we have to compare it to previous MSEs or industry benchmarks is true. Mean Squared Error (MSE) is a measure of the quality of an estimator—it is always non-negative, and values closer to zero are better. In isolation, an MSE value may not be very informative because its magnitude can be influenced by the scale of the data. Therefore, to truly understand the performance of a predictive model or estimation method, one should compare the MSE with other relevant MSEs from previous models or with industry benchmarks. This comparison provides context and helps determine how well the model is performing relative to established standards or alternative approaches.
When performing 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. These are common practices in statistical analysis to identify significant differences or changes under different conditions in paired data.
It's important to note that estimation and the use of statistical measures should always be seen as providing approximate guidelines and that different methods to estimate values such as confidence intervals, p-values, and effect sizes can help in assessing the significance and impact of findings.