Mathematics, 05.05.2021 22:10 carma43
Which diet is best? A fairly recent article in the Journal of the American Medical Association (Dansinger, Griffith, Gleason, et al., 2005) reported on a randomized, comparative experiment in which 160 subjects were randomly assigned to one of four popular diet plans: Atkins, Ornish, Weight Watchers, and Zone (40 subjects per diet). These subjects were recruited through newspaper and television advertisements in the greater Boston area; all were overweight or obese with body mass index values between 27 and 42. Data for the 93 subjects who completed the 12-month study are in data file Diets2. The file contains which diet the subject was on and the weight loss in kilograms (positive values indicate weight loss and negative values indicate weight gain).
a. Identify the explanatory variable and the response variable in this study.
b. What are the observational units in this study?
c. State, in words or symbols, the null and alternative hypotheses.
d. Put the data in the Multiple Means applet and describe what the dotplots tell us about the effectiveness of the four diet plans in aiding weight loss.
e. Using the Multiple Means applet find and report the value of a statistic that summarizes the discrepancies between the four diet plans. What is this statistic called?
f. Using a simulation-based approach, test whether there is evidence of an association between weight loss and diet. Be sure to report a p-value.
g. Based on the p-value reported in part (f), state an appropriate conclusion in the context of the study. Be sure to comment on statistical significance, causation, and generalization along with how you are making your decision.
Answers: 3
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Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?
Answers: 3
Which diet is best? A fairly recent article in the Journal of the American Medical Association (Dans...
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