CHAPTER 6 Big (or Very Large) Data Project 307 Testing a Claim Using a Simulation Based on the Normal Distribution When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger et al., Journal of the American Medical Association, Vol. 293, No. 1). Make the following assumptions: • The amounts of weight lost on the Weight Watchers diet are normally distributed. • The diet has no effect, so the mean amount of weight lost is 0 lb. • The standard deviation of amounts of lost weight is 4.9 lb. • Samples of size n = 40 are randomly selected. Use a technology capable of randomly generating values from a normal distribution with a desired sample size, mean, and standard deviation. Use the technology to randomly generate different samples with the preceding four assumptions. Find the mean of each generated sample. a. Does it appear that the actual sample mean weight loss of 3.0 lb is significantly high? Explain. b. Based on the values of the simulated sample means, what do you conclude about the effectiveness of the diet? Explain. Technology Project 4.Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University). a. Let B denote the event of selecting someone who has blue eyes. What does the event B denote? b. Find the value of P1B2. c. Find the probability of randomly selecting three different people and finding that all of them have blue eyes. d. Find the probability that among 100 randomly selected people, at least 40 have blue eyes. e. If 35% of us really do have blue eyes, is a result of 40 people with blue eyes among 100 randomly selected people a result that is significantly high? 5.Body Temperatures Listed below are body temperatures 1°F2 of adult males (based on Data Set 5 “Body Temperatures” in Appendix B). 97.6 98.2 99.6 98.7 99.4 98.2 980 98.6 98.6 a. Find the mean. Does the result seem reasonable? b. Identify a characteristic of the data that is very notable. c. Based on the result from part (b), what appears to be the mean body temperature of adult males? Big (or Very Large) Data Project Refer to Data Set 45 “Births in New York” in Appendix B. Using the 465,506 birth weights (grams), test for normality. Do the histogram of the birth weights and the normal quantile plot of the birth weights suggest the same conclusion about normality?
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