A student recorded the number of calories in each of 56 entrees -28 vegetarian and 28 non vegetarian - served at a college dining hall.81 The following table summarizes the data. Graphs of the data (not given here) show that both distributions are reasonably symmetric and bell shaped. A 95% confidence interval for µ1 - µ2 is (- 27, 85). For each of the following, say whether the statement is true or false and say why.

(a) 95% of the data are between - 27 and 85 calories.
(b) We are 95% confident that µ1 - µ2 is between -27 and 85 calories.
(c) 95% of the time 1 - 2 will be between - 27 and 85 calories.
(d) 95% of the vegetarian entrees have between 27 fewer calories and 85 more calories than the average non vegetarian entree.

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Vegetarian Nonvegetarian n Mean SD 28 351 119 28 322 87