image 7.38 Food intake and weight gain. 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.18 According to theory, 3500 extra calories will translate into a weight gain of 1 pound. Therefore, we expect each of these subjects to gain 56,000/3500 = 16 pounds (lb). 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

  1. (a) For each subject, subtract the weight before from the weight after to determine the weight change.

  2. (b) Find the mean and the standard deviation for the weight change.

  3. (c) Calculate the standard error and the margin of error for 95% confidence. Report the 95% confidence interval for weight change in a sentence that explains the meaning of the 95%.

  4. (d) Convert the mean weight gain in kilograms to mean weight gain in pounds. Because there are 2.2 kg per pound, multiply the value in kilograms by 2.2 to obtain pounds. Do the same for the standard deviation and the confidence interval.

  5. (e) Test the null hypothesis that the mean weight gain is 16 lb. Be sure to specify the null and alternative hypotheses, the test statistic with degrees of freedom, and the P-value. What do you conclude?

  6. (f) Write a short paragraph explaining your results.