Overweight Children The Ventura County Star (June 20, 2012) reported on a study of children in public schools in California that looked at the proportion of overweight or obese children. In Huntington Park (a small city outside Los Angeles), 53 % of the children were overweight or obese; this was the highest rate found in any city in California. Suppose a random sample of 200 public school children is taken from Huntington Park. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overweight/obese children in the sample will be greater than 0.50. a. Without doing any calculations, determine whether this probability is greater than 50 % or if it is less than 50 % . Explain. b. Calculate the probability that 50 % or more are overweight or obese.
Overweight Children The Ventura County Star (June 20, 2012) reported on a study of children in public schools in California that looked at the proportion of overweight or obese children. In Huntington Park (a small city outside Los Angeles), 53 % of the children were overweight or obese; this was the highest rate found in any city in California. Suppose a random sample of 200 public school children is taken from Huntington Park. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overweight/obese children in the sample will be greater than 0.50. a. Without doing any calculations, determine whether this probability is greater than 50 % or if it is less than 50 % . Explain. b. Calculate the probability that 50 % or more are overweight or obese.
Solution Summary: The author explains that the probability of the proportion of overweight/obese children in the sample will be greater than 0.5 is greater or less than 50%.
Overweight Children The Ventura County Star (June 20, 2012) reported on a study of children in public schools in California that looked at the proportion of overweight or obese children. In Huntington Park (a small city outside Los Angeles),
53
%
of the children were overweight or obese; this was the highest rate found in any city in California. Suppose a random sample of 200 public school children is taken from Huntington Park. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overweight/obese children in the sample will be greater than 0.50.
a. Without doing any calculations, determine whether this probability is greater than
50
%
or if it is less than
50
%
. Explain.
b. Calculate the probability that
50
%
or more are overweight or obese.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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