Question

1. If we increase our food intake, we generally gain weight. Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 nonobese adults, aged 25 to 36 years, were fed 1000 calories per day in excess of the calories needed to maintain a stable body weight. The subjects maintained this diet for eight weeks, so they consumed a total of 56,000 extra calories. According to theory, 3500 extra calories will translate into a weight gain of 1 pound. Therefore, we expect each of these subjects to gain 56000/3500 = 16 pounds. Here are the weights before and after the eight week period, expressed in kilograms (kg):

Subject	1	2	3	4	5	6	7	8
Weight before	55.7	54.9	59.6	62.3	74.2	75.6	70.7	53.3
Weight after	61.7	58.8	66.0	66.2	79.0	82.3	74.3	59.3
Subject	9	10	11	12	13	14	15	16
Weight before	73.3	63.4	68.1	73.7	91.7	55.9	61.7	57.8
Weight after	79.1	66.0	73.4	76.9	93.1	63.0	68.2	60.3

For each subject, subtract the weight before from the weight after to determine the weight change. Report each to one decimal place.

Subject	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Weight change

a) What is the mean of the differences?

b) Find the standard deviation of the differences.

c) Find the standard error for the mean of the differences.

d) Find the margin of error for 95% confidence.

e) Convert the mean weight gain in kilograms to mean weight gain in pounds. There are 0.454 kg per pound. What is the mean of the differences? Report to two decimal places.

f) Find the standard deviation in pounds. Report to two decimal places.

g) What is the new margin of error in pounds? Report to two decimals.

Answer 1

a) The mean of the differences =4.731

b) The standard deviation of the differences.= 1.746

c) The standard error for the mean of the differences.= 1.746/sqrt(16)= 0.4365

d) The margin of error for 95% confidence= tc* S.E= 2.13*0.4365= 0.9297

e) The mean of the differences is 10.43 pounds

f) The standard deviation in pounds. = 3.85 pounds

g) The new margin of error in pounds=2.05 pounds