Does how long young children remain at the lunch table help predict how much they eat? Here are data on a random sample of 20 toddlers observed over several months. “Time” is the average number of minutes a child spent at the table when lunch was served. “Calories” is the average number of calories the child consumed during lunch, calculated from careful observation of what the child ate each day.

Here is some computer output from a least-squares regression analysis of these data. Do these data provide convincing evidence at the α = 0.01 level of a linear relationship between time at the table and calories consumed in the population of toddlers?

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Time Calories Time Calories 21.4 472 42.4 450 30.8 498 43.1 410 37.7 465 29.2 504 33.5 456 31.3 437 32.8 423 28.6 489 39.5 437 32.9 436 22.8 508 30.6 480 34.1 431 35.1 439 33.9 479 33.0 444 43.8 454 43.7 408