To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass for each of seven men. They also measured the total 24-hour energy expenditure for each man during conditions of quiet sedentary activity. The results are shown in the table.10

(a) The correlation between energy expenditure and fat-free mass is very large (near 1). It is 0.98139, but the sample size is quite small, only 7. Is there enough evidence to claim the correlation is different from zero? Carry out an appropriate test using a = 0.05.
(b) Is this study an observational study or an experiment?
(c) Persons who exercise could increase their fat-free mass. Could these data be used to claim that their energy expenditure would also increase? If not, what could be said? Briefly explain.

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Fat-free mass Energy expenditure Subject x X (kg) 49.3 9.3 68.3 48.1 576 78.1 76.1 62.400 12,095 Y (kcal) 1894 2,050 2.353 1,838 1,948 2,568 2.168.429 Mean SD 308.254 0.98139