436 CASE STUDY How Protein Affects Weight Gain in Overeaters 436 CHAPTER 8 Hypothesis Testing with Two Samples In a study published in the Journal of the American Medical Association, three groups of 18- to 35-year-old participants overate for an 8-week period. The groups consumed different levels of protein in their diet. The low protein group’s diet was 5% protein, the normal protein group’s diet was 15% protein, and the high protein group’s diet was 25% protein. The study found that the low protein group gained considerably less weight than the normal protein group or the high protein group. You are a scientist working at a health research firm. The firm wants you to replicate the experiment. You conduct a similar experiment over an 8-week period. The results of the experiment are shown below. EXERCISES In Exercises 1–3, perform a two-sample t-test to determine whether the mean weight gains of the two indicated studies are different. Assume the populations are normally distributed and the population variances are equal. For each exercise, write your conclusions as a sentence. Use a = 0.05. 1. Test the weight gains of the low protein group against those in the normal protein group. 2. Test the weight gains of the low protein group against those in the high protein group. 3. Test the weight gains of the normal protein group against those in the high protein group. 4. In which comparisons in Exercises 1–3 did you find a difference in weight gains? Write a summary of your findings. 5. Construct a 95% confidence interval for m1 - m2, where m1 is the mean weight gain in the normal protein group and m2 is the mean weight gain in the high protein group. Assume the populations are normally distributed and the population variances are equal. (See Extending Concepts in Section 8.2 Exercises.) Low protein group Normal protein group High protein group Weight gain (after 8 weeks) x1 = 6.8 lb s1 = 1.7 lb n1 = 12 x2 = 13.5 lb s2 = 2.5 lb n2 = 16 x3 = 14.2 lb s3 = 2.1 lb n3 = 15
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